Question

Fill in the blank. In the triangle below, y = _. Round your answer to two decimal places.

Answer 1

Y will be approximately 47.10 in length

Explanation:

• we will use this form that we memorized in our schools ............. SOH CAH TOA

CAH means , Cos ∅= Adjacent/Hypotenuse

• Given values

∅ =42°

hypotenuse= y

adjacent side length = 35

• now putting in our values into

Cos ∅= Adjacent/Hypotenuse

OR

cos(42°) = 35/y

• by multiplying y on both sides we get

y= 35/cos( 42°)

• cos(42°)= 0.743

so y= 35/0.743

y = 47.10632

OR

• y ≈ 47.10

Answer 2

47.10

Explanation:

The mnemonic SOH CAH TOA reminds you that ...

... Cos = Adjacent/Hypotenuse

The value y is the length of the hypotenuse, and the given length 35 is the side adjacent to the given angle. Thus, the cosine relationship will be helpful.

Filling in the given values, we have ...

... cos(42°) = 35/y

Multiplying by y/cos(42°), we can find y to be ...

... y = 35/cos(42°) ≈ 35/0.7431

... y ≈ 47.10