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Vinvika [58]
2 years ago
9

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

Mathematics
2 answers:
nydimaria [60]2 years ago
6 0

Answer:

a = 56.3°

Step-by-step explanation:

tan(a) = 9/6 = 1.5

atan(1.5) = 56.31°

Gnom [1K]2 years ago
4 0

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.

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