Question

In a right triangle the two legs are measures of 4x and 3x with a hypotenuse measurement of 5x. If the area of the triangle is 24 square units, find the cosine of each acute angle.

Answer 1

The cosine of the acute angles are 0.80 and 0.60 respectively

The given parameters are:

$Leg\ 1 = 4x$

$Leg\ 2 = 3x$

$Hypotenuse = 5x$

Let the acute angles be $\alpha$ and $\beta$

The cosine of the acute angles is calculated using:

$\cos(\alpha) = \frac{Leg\ 1}{Hypotenuse}$

$\cos(\beta) = \frac{Leg\ 2}{Hypotenuse}$

So, the formula becomes

$\cos(\alpha) = \frac{4x}{5x}$

$\cos(\alpha) = \frac{4}{5}$

$\cos(\alpha) = 0.80$

and

$\cos(\beta) = \frac{3x}{5x}$

$\cos(\beta) = \frac{3}{5}$

$\cos(\beta) = 0.60$

Hence, the cosine of the acute angles are 0.80 and 0.60 respectively

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