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]
