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

there are videos on you tube if you wanna check them out

Explanation:  

The temperature of lava is so high that the moment it comes in contact with ice, it converts the latter directly into vapor, without turning it into water first. This steam essentially tries to escape through the lava.