Question

Consider a right triangle with leg b = 7.1 and opposite angle B = 39.3. Using a calculator, determine the other angle and the remaining sides of the triangle. Express your answers using at least one decimal place.

Answer 1

Answer:

i. a = 8.7, b = 7.1 and c = 11.2

ii. A = $50.7^{o}$, B = $39.3^{o}$ and C = $90^{o}$

Step-by-step explanation:

Given a right triangle with, b = 7.1 and B = $39.3^{o}$.

I. Applying the trigonometric function to determine leg a, we have;

Tan θ = $\frac{opposite}{adjacent}$

Tan $39.3^{o}$ = $\frac{7.1}{a}$

a = $\frac{7.1}{Tan 39.3^{o} }$

  = 8.675

The length of leg a is 8.7.

ii. To determine leg c,

Sin $39.3^{o}$ = $\frac{opposite}{hypotenuse}$

              = $\frac{7.1}{c}$

⇒c = $\frac{7.1}{Sin39.3^{o} }$

     = 11.21

The length of leg c is 11.2.

iii. Given that: B = $39.3^{o}$ and C = $90^{o}$

Then,

A + B + C = $180^{o}$  (sum of angles at a point)

A + $39.3^{o}$ + $90^{o}$ = $180^{o}$

A + $129.3^{o}$ = $180^{o}$

A = $180^{o}$ - $129.3^{o}$

  = $50.7^{o}$