Question

1 Х 15 8 sin-1 8 =mZT 15 T 17 U

Answer 1

Given:

In a right angled traingle with hypotenuse 17.

The other two length of the sides are 15 and 8.

The objective is to find the correct way of finding the angle T.

While solving a trigonometric ratio, the hypotenuse always present opposite to angle. 90 degree.

The opposite side of the triangle depends on the angle which we have to find out.

In this case, the objective is to find the measure of angle T.

So, the side opposite to angle T will be named as opposite side of right angled triangle and the reminig side will be named as adjacent side of the right angled triangle.

Since, the formula of sin is,

`\sin \theta=\frac{opposite\text{ }}{hypotenuse}`

If T is the angle, then opposite side is 8 and the hypotenuse is 17.

So the correct formula will be,

`\begin{gathered} \sin \angle T=(8)/(17) \\ \angle T=\sin ^(-1)(8)/(17) \\ \angle T=\sin ^(-1)0.47058 \\ \angle T=28.07 \end{gathered}`

Hence, the correct correct value is sin^-1 (8/17) and the measure of angle T is 28.07.