Question

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Answer 1

The trigonometric function gives the ratio of different sides of a right-angle triangle. The measure of ∠C is 28°. And the value of b and c is 7.06 and 3.76, respectively.

What are Trigonometric functions?

The trigonometric function gives the ratio of different sides of a right-angle triangle.

$\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}$

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite the 90° angle.

The sum of all the angles can be written as,

∠A + ∠B + ∠C = 180°

90° + 62° + ∠C = 180°

∠C = 28°

Sin(∠B) = AC/BC

Sin(∠B) = b/8

b = 8 × Sin(62°)

b = 7.06

Cos(∠B) = AB/BC

Cos(∠B) = c/8

c = 8 × Cos(62°)

c = 3.76

Hence, the measure of ∠C is 28°. And the value of b and c is 7.06 and 3.76, respectively.

Learn more about Trigonometric functions:

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