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

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:

$Sin \theta = \dfrac{opposite}{hypothenuse}$

∴

$Sin (53^0) = \dfrac{4}{x}$

Making x the subject of the formula:

$x = \dfrac{4}{Sin \ 53^0}$

$x = \dfrac{4}{0.7986}$

$x \simeq 5$

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

Recall that:

$Cos \theta = \dfrac{adjacent}{hypothenuse}$

$Cos \ 53^0 = \dfrac{y}{x}$

where; x = 5

$Cos \ 53^0 = \dfrac{y}{5}$

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

Answer 2

Answer:

simple answer B

Step-by-step explanation: