MATH SOLVE

4 months ago

Q:
# 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 EndFractioncos(53o) = StartFraction y Over 5 EndFractioncos(53o) = StartFraction x Over 4 EndFractioncos(53o) = StartFraction 5 Over y EndFraction

Accepted Solution

A:

Answer:cos(53°)=StartFraction y Over 5 EndFractionStep-by-step explanation:see the attached figure to better understand the problemstep 1Find the value of xwe know that[tex]sin(53\°)=\frac{4}{x}[/tex]Solve for x[tex]x=\frac{4}{sin(53\°)}[/tex][tex]x=5[/tex]step 2Find the cosine of angle AThe cosine of angle A is equal to divide the adjacent side to angle A (AC) by the hypotenuse (AB)[tex]cos(53\°)=\frac{y}{x}[/tex]substitute the value of x[tex]cos(53\°)=\frac{y}{5}[/tex]socos(53°)=StartFraction y Over 5 EndFraction