Question

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

simple answer B

Explanation:

Answer 2

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

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 = (opposite)/(hypothenuse)`

∴

`Sin (53^0) = (4)/(x)`

Making x the subject of the formula:

`x = (4)/(Sin \ 53^0)`

`x = (4)/(0.7986)`

`x \simeq 5`

Now, the equation that correctly uses the value of x can be determined by finding the cosine of ∠ A.

Recall that:

`Cos \theta = (adjacent)/(hypothenuse)`

`Cos \ 53^0 = (y)/(x)`

where; x = 5

`Cos \ 53^0 = (y)/(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