Question

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

Answer 1

Answer:

a = 56.3°

Step-by-step explanation:

tan(a) = 9/6 = 1.5

atan(1.5) = 56.31°

Answer 2

Answer:

$\boxed {\boxed {\sf 56.3 \textdegree}}$

Step-by-step 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.

$tan \theta= \frac{ opposite}{adjacent}$

$tan \ a = \frac{ 9}{6}$

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.