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:

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

ii. A = [tex]50.7^{o}[/tex], B = [tex]39.3^{o}[/tex] and C = [tex]90^{o}[/tex]

Step-by-step explanation:

Given a right triangle with, b = 7.1 and B = [tex]39.3^{o}[/tex].

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

Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

Tan [tex]39.3^{o}[/tex] = [tex]\frac{7.1}{a}[/tex]

a = [tex]\frac{7.1}{Tan 39.3^{o} }[/tex]

  = 8.675

The length of leg a is 8.7.

ii. To determine leg c,

Sin [tex]39.3^{o}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]

              = [tex]\frac{7.1}{c}[/tex]

⇒c = [tex]\frac{7.1}{Sin39.3^{o} }[/tex]

     = 11.21

The length of leg c is 11.2.

iii. Given that: B = [tex]39.3^{o}[/tex] and C = [tex]90^{o}[/tex]

Then,

A + B + C = [tex]180^{o}[/tex]  (sum of angles at a point)

A + [tex]39.3^{o}[/tex] + [tex]90^{o}[/tex] = [tex]180^{o}[/tex]

A + [tex]129.3^{o}[/tex] = [tex]180^{o}[/tex]

A = [tex]180^{o}[/tex] - [tex]129.3^{o}[/tex]

  = [tex]50.7^{o}[/tex]

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A
54° and 36° are complementary angles in the same right triangle. sin54° is the ratio of the opposite leg and the hypotenuse and cos36° is the ratio of the adjacent leg and the hypotenuse. In this triangle, the opposite leg of 54° and the adjacent leg of 36° are the same leg in the triangle.

B
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D
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