A right triangle has sides 10 m,5 m,and 11 m.The smallest angle of this triangle is nearest
A)32°.
B)27°.
C)22°.
D)63°.
E)Not attainable since this is not a right triangle.

Question

A right triangle has sides 10 m,5 m,and 11 m.The smallest angle of this triangle is nearest
A)32°.
B)27°.
C)22°.
D)63°.
E)​Not attainable since this is not a right triangle.

Quizplus · Accepted Answer

In a right triangle, the longest side is always the hypotenuse. We have 11 m as the longest side and it is opposite to the right angle. The other two sides are 10 m and 5 m. To find the smallest angle, we need to use trigonometric ratios.

Let's use the sine ratio:

$$\sin	heta = \frac{	ext{opposite}}{	ext{hypotenuse}}$$

We want to find the angle $	heta$ that is opposite to the shortest side (5 m). So, we have:

$$\sin	heta = \frac{5}{11}$$

Taking the inverse sine of both sides, we get:

$$	heta = \sin^{-1} \left(\frac{5}{11}ight) \approx 27^\circ$$

Therefore, the smallest angle is about 27°, which is closest to choice B.

A Right Triangle Has Sides 10 M,5 M,and 11 M