Here is the full question:
Triangle ABC is a right-triangle and sin(53o) = StartFraction 4 Over x EndFraction. Solve for x & 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 use the value of x to represents 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:
cos(53°) = StartFraction y Over 5 EndFraction
Step-by-step explanation:
From the information above:
The sketch of the triangle is drawn and attached in the diagram below.
To find x using the sine rule,
We know that:
![Sin \theta = \dfrac{opposite}{hypothenuse}](https://tex.z-dn.net/?f=Sin%20%5Ctheta%20%3D%20%5Cdfrac%7Bopposite%7D%7Bhypothenuse%7D)
∴
![Sin (53^0) = \dfrac{4}{x}](https://tex.z-dn.net/?f=Sin%20%2853%5E0%29%20%3D%20%5Cdfrac%7B4%7D%7Bx%7D)
Making x the subject of the formula:
![x = \dfrac{4}{Sin \ 53^0}](https://tex.z-dn.net/?f=x%20%3D%20%5Cdfrac%7B4%7D%7BSin%20%5C%2053%5E0%7D)
![x = \dfrac{4}{0.7986}](https://tex.z-dn.net/?f=x%20%3D%20%5Cdfrac%7B4%7D%7B0.7986%7D)
![x \simeq 5](https://tex.z-dn.net/?f=x%20%5Csimeq%205)
Now, the equation that correctly uses the value of x can be determined by finding the cosine of ∠ A.
Recall that:
![Cos \theta = \dfrac{adjacent}{hypothenuse}](https://tex.z-dn.net/?f=Cos%20%5Ctheta%20%3D%20%5Cdfrac%7Badjacent%7D%7Bhypothenuse%7D)
![Cos \ 53^0 = \dfrac{y}{x}](https://tex.z-dn.net/?f=Cos%20%5C%2053%5E0%20%3D%20%5Cdfrac%7By%7D%7Bx%7D)
where; x = 5
![Cos \ 53^0 = \dfrac{y}{5}](https://tex.z-dn.net/?f=Cos%20%5C%2053%5E0%20%3D%20%5Cdfrac%7By%7D%7B5%7D)
Thus, the equation that correctly uses the value of x to represent the cosine of angle A is:
cos(53°) = StartFraction y Over 5 EndFraction