In a right triangle, the 58-cm hypotenuse makes a 51-degree angle with one of the legs. To the nearest
tenth of a cm, how long is that leg?

Respuesta :

Answer:

36.5 cm

Step-by-step explanation:

The Adjacent leg is 36.5 cm

What are trigonometric functions?

"The trigonometric functions (also called circular functions, angle functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths."

What is hypotenuse, opposite and adjacent side of a right angled triangle?

"In a right angled triangle, the hypotenuse is the longest side, an opposite side is the one across from a given angle, and an adjacent side is next to a given angle."

We have

Hypotenuse (AB) = 58 cm

Angle θ = 51 degree

From the figure, by using trigonometric functions

Cos θ = [tex]\frac{BC}{AB}[/tex]

we have to find BC

Cos [tex]51^{0}[/tex] = [tex]\frac{BC}{AB}[/tex]

We have, AB = 58 cm

BC = AB cos [tex]51^{0}[/tex]

⇒BC = 58 . cos [tex]51^{0}[/tex]

⇒BC = 36.50 cm

⇒BC = 36.5 cm

Hence, Adjacent leg is 36.5 cm

Learn more about trigonometric functions here

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