If m 90 ° in the triangle shown, then sin .

Question

If m  90 ° in the triangle shown, then sin  .

Quizplus · Accepted Answer

In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite to that angle to the length of the hypotenuse. Since we know that one angle in the triangle is 90°, we can use trigonometric ratios to find the lengths of the sides.

Let's assume that the side opposite to the angle is 'a' and the hypotenuse is 'h'. Then, using the Pythagorean theorem, we can find the length of the third side. It would be √(h^2 - a^2).

Now, if the angle opposite to 'a' is 11ebfb55_24cb_a5a2_9d86_c543a558a02e_TBX8811_11, we can use the definition of sine to find sin 11ebfb55_24cb_a5a2_9d86_c543a558a02e_TBX8811_11.

sin 11ebfb55_24cb_a5a2_9d86_c543a558a02e_TBX8811_11 = (length of side opposite to 11ebfb55_24cb_a5a2_9d86_c543a558a02e_TBX8811_11) / (length of hypotenuse)

Using the ratio we assumed earlier,

sin 11ebfb55_24cb_a5a2_9d86_c543a558a02e_TBX8811_11 = a/h

Since we know that the triangle has a 90° angle, we can use the given angle of 11ebfb55_24cb_a5a1_9d86_8993eb93fd0d_TBX8811_11 (which is complementary to 11ebfb55_24cb_a5a2_9d86_c543a558a02e_TBX8811_11) to find the ratio of 'a' and 'h'.

If the given angle is 90°, then sin(11ebfb55_24cb_a5a1_9d86_8993eb93fd0d_TBX8811_11) = 1.

By the definition of complementary angles, we know that:

sin(11ebfb55_24cb_a5a1_9d86_8993eb93fd0d_TBX8811_11) = cos(11ebfb55_24cb_a5a2_9d86_c543a558a02e_TBX8811_11)

So, we can write:

cos(11ebfb55_24cb_a5a2_9d86_c543a558a02e_TBX8811_11) = 1

Using the trigonometric identity:

sin^2 x + cos^2 x = 1

We get:

sin^2(11ebfb55_24cb_a5a2_9d86_c543a558a02e_TBX8811_11) + 1^2 = 1

Simplifying this further:

sin^2(11ebfb55_24cb_a5a2_9d86_c543a558a02e_TBX8811_11) = 0

Taking the square root of both sides, we get:

sin(11ebfb55_24cb_a5a2_9d86_c543a558a02e_TBX8811_11) = 0

Therefore, the answer is A) True.

If M 90 ° in the Triangle Shown, Then