Question

Find a (Round to the nearest tenth). PLS HURRY!!

Answer 1

a = 56.3°

Explanation:

tan(a) = 9/6 = 1.5

atan(1.5) = 56.31°

Answer 2

`\boxed {\boxed {\sf 56.3 \textdegree}}`

Explanation:

We are asked to find the measure of angle a.

This triangle is a right triangle because of the small triangle in the corner representing a 90 degree or right angle. Therefore, we can use trigonometric functions. The three main functions are:

• sinθ=opposite/hypotenuse
• cosθ= adjacent/hypotenuse
• tanθ= opposite/adjacent

The side measuring 6 is adjacent or next to angle a. The side measuring 9 is opposite angle a. Therefore, we will use the tangent function.

`tan \theta= ( opposite)/(adjacent)`

`tan \ a = ( 9)/(6)`

Since we are solving for an angle measure, we use the inverse trigonometric function.

`tan ^(-1) * tan \ a = tan ^(-1) * \frac{9}6}`

`a= tan ^(-1) * \frac{9}6}`

`a= 56.30993247`

Round to the nearest tenth. The 0 in the hundredth place tells us to leave the 3 in the tenth place.

`a \approx 56.3`

The measure of angle a is approximately 56.3 degrees.