Question

Triangle ABC is a right triangle and sin(53o) = StartFraction 4 Over x EndFraction. Solve for x and round to the nearest whole number.
Triangle A B C is shown. Angle A C B is a right angle and angle B A C is 53 degrees. The length of B C is 4 centimeters, the length of A C is y, and the length of hypotenuse A B is x.

Which equation correctly uses the value of x to represent the cosine of angle A?

cos(53o) = StartFraction 4 Over x EndFraction
cos(53o) = StartFraction y Over 5 EndFraction
cos(53o) = StartFraction x Over 4 EndFraction
cos(53o) = StartFraction 5 Over y EndFraction

Answer 1

Answer:

cos(53°)=StartFraction y Over 5 EndFraction

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the value of x

we know that

$sin(53\°)=\frac{4}{x}$

Solve for x

$x=\frac{4}{sin(53\°)}$

$x=5$

step 2

Find the cosine of angle A

The cosine of angle A is equal to divide the adjacent side to angle A (AC) by the hypotenuse (AB)

$cos(53\°)=\frac{y}{x}$

substitute the value of x

$cos(53\°)=\frac{y}{5}$

so

cos(53°)=StartFraction y Over 5 EndFraction