What is the value of z in the triangle? enter your answer in the box. round your final answer to the nearest hundredth. z = in. a right triangle. one angle measures 37 degrees. the side adjacent to the 37-degree angle measures 10 inches. the hypotenuse is labeled as z.

z = 12.53 inches.

Step-by-step explanation:

Given : A right triangle. One angle measures 37 degrees. The side adjacent to the 37-degree angle measures 10 inches. The hypotenuse is labeled as z.

TO find : What is the value of z in the triangle? Enter your answer in the box. Round your final answer to the nearest hundredth.

Solution : We have given that a right triangle with one angle 37 degree and  

side adjacent of 37 degree = 10 inches

Hypotenuse =  z

By the cosine ration :

Cos (Ф) =

plugging the values of adjacent side and hypotenuse

Cos (37) =

On multiplying both side by z

z (0.798) = 10

On dividing by 0.798 both sides

z =

z = 12.53 inches.

Therefore, z = 12.53 inches.

Applying the trigonometry ratio, CAH, the value of z is: 12.5 inches.

Trigonometry ratio for solving a right triangle is given as SOH CAH TOA.

Thus:

Apply CAH:

Cos ∅ = adj/hyp

cos 37 = 10/z

z = 10/(cos 37)

z = 12.5 inches.

Learn more about the trigonometry ratio on:

link

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step-by-step explanation: