Question

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Answer 1

Answer:

The length of AB is approximately 6.07 m

Step-by-step explanation:

The given dimensions of the triangle are;

The value of x = 7.7 m

The measure of angle, θ = 52°

The length of side AB = Required

The given triangle ΔABC is a right triangle, with the following sides;

AC = x = The hypotenuse (opposite to right angle) side

(Leg) AB = The opposite side to the reference angle, θ

(Leg) BC = The adjacent side to the reference angle, θ

By trigonometric ratio, we have;

$sin(\theta) = \dfrac{Opposite \ leg \ length}{Hypotenuse \ length} = \dfrac{AB}{x}$

Therefore;

$sin(52^{\circ}) = \dfrac{AB}{7.7}$

AB = 7.7 × sin(52°) ≈ 6.07

The length of AB ≈ 6.07 m.