Question 1

The two figures are congruent. Find the measure of the requested side or angle.
-$\angle \mathrm { B } ^ { \prime } \mathrm { C } ^ { \prime } \mathrm { D } ^ { \prime }$

Accepted Answer

The answer of The two figures are congruent. Find the...

Question 2

Solve the problem.
-Hye-Ran, who is 1.60 m tall, wishes to find the height of a tree with a shadow 30.06 m long. She Walks 21.65 m from the base of the tree along the shadow of the tree until her head is in a position Where the tip of her shadow exactly overlaps the end of the tree topʹs shadow. How tall is the tree? Round to the nearest hundredth.

Accepted Answer

The answer of Solve the problem.
-Hye-Ran, who is 1.60 m...

Question 3

The two figures are congruent. Find the measure of the requested side or angle.
-$\angle \mathrm { ABC }$

Accepted Answer

The answer of The two figures are congruent. Find the...

Question 4

Solve the problem.
-A triangle drawn on a map has sides of lengths 9.0 cm, 12 cm, and 15 cm. The shortest of the Corresponding real-life distances is 90 km. Find the longest of the real-life distances. Round to the Nearest unit.

Accepted Answer

The scale factor for the map to real-life conversion is found by dividing the real-life distance by the map distance for the shortest side: 90 km / 9.0 cm = 10 km/cm. The longest side on the map is 15 cm, so the longest real-life distance is 15 cm * 10 km/cm = 150 km.

Question 5

The two figures are congruent. Find the measure of the requested side or angle.
-The length of $\overline { C D }$

Accepted Answer

The answer of The two figures are congruent. Find the...

Question 6

The two figures are congruent. Find the measure of the requested side or angle.
-$\angle B C D$

Accepted Answer

The answer of The two figures are congruent. Find the...

Question 7

Find the area.
-

Accepted Answer

The answer of Find the area.
-
...

Question 8

Solve the problem.
-A line from the top of a cliff to the ground passes just over the top of a pole 8.0 ft high and meets The ground at a point 5.0 ft from the base of the pole. If the point is 99 ft from the base of the cliff, How high is the cliff? Round to the nearest unit.

Accepted Answer

The problem can be solved using similar triangles. The line from the top of the cliff to the ground creates a right triangle with the ground and the height of the cliff as its sides. The pole and its distance from the point where the line meets the ground create a smaller, similar triangle. The ratio of the height of the cliff to the total distance from its base to the point where the line meets the ground (99 ft + 5 ft = 104 ft) is the same as the ratio of the height of the pole (8 ft) to its distance from the point where the line meets the ground (5 ft). Therefore, the height of the cliff is to 104 ft as 8 ft is to 5 ft. Solving for the height of the cliff (h) gives us h/104 = 8/5, so h = (8/5) * 104 = 166.4 ft, which rounds to 158 ft to the nearest unit.

Question 9

Solve the problem.
-A lake lies between $\mathrm { A }$ and $\mathrm { C }$, and lines $\mathrm { AB }$ and $\mathrm { DE }$ run north-south. If $\overline { \mathrm { AB } } = 7.1 \mathrm { mi }$, $\overline { \mathrm { DE } } = 1.5 \mathrm { mi }$, and $\overline { \mathrm { DC } } = 1.4 \mathrm { mi }$, how far is it from $\mathrm { A }$ to $\mathrm { C }$ ? Round to the nearest tenth.

Accepted Answer

The answer of Solve the problem.
-A lake lies between \(\mathrm...

Question 10

Solve the problem.
-In order to measure the distance across a pond (from A to B), Raul made some measurements, Which are given below the drawing. What is the distance (to the nearest unit)?

$\angle \mathrm { ABE } = 50 ^ { \circ } , \overline { \mathrm { BE } } = 167 \mathrm { ft } , \overline { \mathrm { ED } } = 49 \mathrm { ft } , \overline { \mathrm { DC } } = 41 \mathrm { ft } , \overline { \mathrm { CE } } = 54 \mathrm { ft } , \angle \mathrm { DCE } = 50 ^ { \circ }$

Accepted Answer

The answer of Solve the problem.
-In order to measure the...

Question 11

Solve the problem.
-Mieko, who is 1.67 m tall, wishes to find the height of a tree. She walks 22.93 m from the base of The tree along the shadow of the tree until her head is in a position where the tip of her shadow Exactly overlaps the end of the tree topʹs shadow. She is now 7.87 m from the end of the shadows. How tall is the tree? Round to the nearest hundredth.

Accepted Answer

The answer of Solve the problem.
-Mieko, who is 1.67 m...

Question 12

The two figures are congruent. Find the measure of the requested side or angle.
-$$\angle \mathrm { B } ^ { \prime } \mathrm { A } ^ { \prime } \mathrm { D } ^ { \prime }$$

Accepted Answer

The answer of The two figures are congruent. Find the...

Question 13

Find the area.
-

Accepted Answer

The answer of Find the area.
-
...

Question 14

Solve the problem.
-A church steeple casts a shadow 103 ft long, and at the same time a 8.0-ft post casts a shadow 5.0 ft Long. How high is the steeple? Round to the nearest unit.

Accepted Answer

The steeple is 165 ft high.

Question 15

Find the area.
-

Accepted Answer

The answer of Find the area.
-
...

Question 16

Solve the problem.
-A statue is 61-cm tall. When its shadow is 100 cm long, the shadow of a certain tree is 16 m long. How tall is the tree? Round to the nearest unit.

Accepted Answer

The answer of Solve the problem.
-A statue is 61-cm tall....

Question 17

The two figures are congruent. Find the measure of the requested side or angle.
-The length of $\overline { \mathrm { B } ^ { \prime } \mathrm { C } ^ { \prime } }$

Accepted Answer

The answer of The two figures are congruent. Find the...

Question 18

Solve the problem.
-To find the height of this tree, Luis marked the tree at eye level, 1.8 meters above the ground. He Measured 35 m from the base of the tree and then held a 5-cm ruler vertically in front of his eye Until the ruler just obscured the tree above the mark. Using a string tied through a hole in one end Of the ruler, Luis found that the distance from his eye to the ruler was 5.1 centimeters. What was The height of the tree? Round to the nearest meter.

Accepted Answer

The answer of Solve the problem.
-To find the height of...

Question 19

The two figures are congruent. Find the measure of the requested side or angle.
-$\overline{\mathrm{A}^{\prime} \mathrm{C}^{\prime}}$

Accepted Answer

The answer of The two figures are congruent. Find the...

Question 20

Solve the problem.
-On a cloudy day, Luciane needed to know the height of a window in a building. Luciane Positioned a mirror on the ground between herself and the building so that when he looked in the Mirror, she saw the window. If the mirror was 22.32 cm from her feet and 35.3 m from the base of The building and Lucianeʹs eye was 1.76 m above the ground, how high up on the building was the Window located? Round to the nearest meter.

Accepted Answer

The mirror forms an image of the window that is the same height as the window and the same distance from the mirror as the window is from the building. So, the height of the window is equal to the distance from Luciane's eye to the mirror plus the distance from the mirror to the building. This is 1.76 m + 35.3 m = 37.06 m. Rounding to the nearest meter, the height of the window is 37 m.

Quiz 8: The Metric System

Solve the problem. -A triangle drawn on a map has sides of lengths 9.0 cm, 12 cm, and 15 cm. The shortest of the Corresponding real-life distances is 90 km. Find the longest of the real-life distances. Round to the Nearest unit.

Find the area. - $Find the area. - A) 200 \mathrm {~cm} ^ { 2 } B) 380 \mathrm {~cm} ^ { 2 } C) 250 \mathrm {~cm} ^ { 2 } D) 760 \mathrm {~cm} ^ { 2 }$

Solve the problem. -A line from the top of a cliff to the ground passes just over the top of a pole 8.0 ft high and meets The ground at a point 5.0 ft from the base of the pole. If the point is 99 ft from the base of the cliff, How high is the cliff? Round to the nearest unit.

Find the area. - $Find the area. - A) 532 \mathrm { yd } ^ { 2 } B) 1064 \mathrm { yd } ^ { 2 } C) 722 \mathrm { yd } ^ { 2 } D) 779 \mathrm { yd } ^ { 2 }$

Solve the problem. -A church steeple casts a shadow 103 ft long, and at the same time a 8.0-ft post casts a shadow 5.0 ft Long. How high is the steeple? Round to the nearest unit.

Find the area. -

Solve the problem. -A statue is 61-cm tall. When its shadow is 100 cm long, the shadow of a certain tree is 16 m long. How tall is the tree? Round to the nearest unit.

Quiz 8: The Metric System

The two figures are congruent. Find the measure of the requested side or angle. - ∠B′C′D′\angle \mathrm { B } ^ { \prime } \mathrm { C } ^ { \prime } \mathrm { D } ^ { \prime }∠B′C′D′

The two figures are congruent. Find the measure of the requested side or angle. - ∠ABC\angle \mathrm { ABC }∠ABC

Solve the problem. -A triangle drawn on a map has sides of lengths 9.0 cm, 12 cm, and 15 cm. The shortest of the Corresponding real-life distances is 90 km. Find the longest of the real-life distances. Round to the Nearest unit.

The two figures are congruent. Find the measure of the requested side or angle. -The length of CD‾\overline { C D }CD

The two figures are congruent. Find the measure of the requested side or angle. - ∠BCD\angle B C D∠BCD

Find the area. -

Solve the problem. -A line from the top of a cliff to the ground passes just over the top of a pole 8.0 ft high and meets The ground at a point 5.0 ft from the base of the pole. If the point is 99 ft from the base of the cliff, How high is the cliff? Round to the nearest unit.

The two figures are congruent. Find the measure of the requested side or angle. - ∠B′A′D′\angle \mathrm { B } ^ { \prime } \mathrm { A } ^ { \prime } \mathrm { D } ^ { \prime }∠B′A′D′

Find the area. -

Solve the problem. -A church steeple casts a shadow 103 ft long, and at the same time a 8.0-ft post casts a shadow 5.0 ft Long. How high is the steeple? Round to the nearest unit.

Find the area. -

Solve the problem. -A statue is 61-cm tall. When its shadow is 100 cm long, the shadow of a certain tree is 16 m long. How tall is the tree? Round to the nearest unit.

The two figures are congruent. Find the measure of the requested side or angle. -The length of B′C′‾\overline { \mathrm { B } ^ { \prime } \mathrm { C } ^ { \prime } }B′C′

The two figures are congruent. Find the measure of the requested side or angle. - A′C′‾\overline{\mathrm{A}^{\prime} \mathrm{C}^{\prime}}A′C′

Find the area. - $Find the area. - A) 200 \mathrm {~cm} ^ { 2 } B) 380 \mathrm {~cm} ^ { 2 } C) 250 \mathrm {~cm} ^ { 2 } D) 760 \mathrm {~cm} ^ { 2 }$

Find the area. - $Find the area. - A) 532 \mathrm { yd } ^ { 2 } B) 1064 \mathrm { yd } ^ { 2 } C) 722 \mathrm { yd } ^ { 2 } D) 779 \mathrm { yd } ^ { 2 }$