Answer:
x = 7.3
Step-by-step explanation:
We're going to use the formula for the area of a triangle:
Area = 1/2 x base x height
We can see that the height of the triangle is 10, but we don't know what the base length is.
We know that one of the angles is 54 °, so we're going to use SOH CAH TOA to work out the length of the base.
We're using the height and the base, which are the opposite (O) and adjacent (A) sides relative to our angle. According to SOH CAH TOA we'll use tan (T).
The equation is tan(Ф°) = O/A, where Ф is our angle (54°), O is our opposite side (10), and A is our adjacent side. Since we don't know what A is we'll use x.
tan (54°) = 10/x
Multiply both sides of the equation by x.
x tan (54°) = 10
Divide both sides of the equation by tan(54°).
x = 10/tan(54°)
Use your calculator to solve for x.
x = 7.265
To the nearest tenth, x = 7.3
