We know that the length of the shortest side of a right triangle is 8.4 meters and the length of the hypotenuse is 12.9 meters. We are asked to find the measure of the acute angles. Let's start by denoting the first angle as θ.
To find its measure, we can recall the trigonometric ratio for cosine.
cos θ = Adjacent/HypotenuseIn this case, the length of the side adjacent to θ is 8.4 meters and the length of the hypotenuse is 12.9 meters.
cos θ = Adjacent/Hypotenuse ⇒ cos θ= 8.4/12.9
We will use this equation to find θ. To do so, we will apply the inverse function for cosine on each side of this equation.
Notice that we have two angles, 49.4^(∘) and 90^(∘). Therefore, we can find the measure of the last angle using the Triangle Angle Sum Theorem.
Triangle Angle Sum Theorem
The sum of measures of the interior angles of any triangle is 180^(∘).
If we denote the measure of the missing acute angle by α, we can write the following equation.
90^(∘) + 49.4^(∘) + α = 180 ^(∘)
Let's solve it for α!
