Answer:
h = 7.9 cm
Step-by-step explanation:
Pre-Solving
We are given that a right triangle has one of its acute angles equal to 26°. We also know that the hypotenuse is 18 cm, and one of the legs is h cm. We want to find the value of h.
We can use the trigonometric ratios in order to find the value of h.
Recall the three most common ratios:
[tex]sinx = \frac{oppsite}{hypotenuse}[/tex]
[tex]cosx=\frac{adjacent}{hypotenuse}[/tex]
[tex]tanx=\frac{opposite}{adjacent}[/tex]
We need to have an angle that we will reference in order to figure out which side is the opposite and which one is the adjacent. The angle shall be the 26° one.
So, in reference to the 26 degree angle, the opposite side is the side labeled h and the adjacent is the unmarked leg.
So, we will use sine in order to find h.
Solving
The sin of 26 degrees is equal to [tex]\frac{h}{18}[/tex].
So:
sin26 = [tex]\frac{h}{18}[/tex]
Multuiply both sides by 18.
18sin26 = h
Plug 18sin26 into your calculator and make sure your calculator is in degree mode.
h ≈ 7.9 cm
