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:
∴
Making x the subject of the formula:
Now, the equation that correctly uses the value of x can be determined by finding the cosine of ∠ A.
Recall that:
where; x = 5
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
