Use the trigonometric ratio for tangent. Then, add the length of the both opposite sides to find the total length.
20.3 square meters
Practice makes perfect
We know that an altitude of 5 meters inside a triangle forms 36^(∘) and 42^(∘) angles with two of the sides.
As we can see, the altitude divides the triangle in two right triangles. Since we have the measure of the angles, we can calculate the length of A and B by using the trigonometric ratio for tangent.
tan θ = Opposite/AdjacentWe will begin with the side A. Here, the measure of the angle is 36^(∘), the length of the adjacent side is 5, and the length of the opposite side is A.
tan θ = Opposite/Adjacent ⇒ tan 36^(∘) = A/5
Let's solve this equation to obtain the value of A.
Next, we will do the same for the side B. This time, the measure of the angle is 42^(∘), the length of adjacent side is 5, and the length of the opposite side is B.
tan 42^(∘) = B/5
Let's solve this equation to get the value of B.
Now that we have the length of each opposite side, we can sum them to obtain the total length of the base of the big triangle.
base = A + B ⇒ base = 8.1 meters
Finally, we will recall the formula for the area of a triangle.
Area = 1/2 ( b* h)
In this equation, b is the length of the base and h is the height of the triangle. We will substitute b= 8.1 and h= 5 into the formula to find the area.
