Answer:
Length of DE = 22.8cm
Step-by-step explanation:
Given: 23° and 8.9cm
To find the length of DE, we need to use the SOH-CAH-TOA method.
Since DE is the hypotenuse (The longest side), we need to use SOH meaning sinФ([tex]\frac{opposite}{hypotenuse}[/tex]).
The opposite of the angle, 23° is 8.9cm, by replacing the formula with the given, we would get the following: sin(23°)=([tex]\frac{8.9}{x}[/tex]).
To calculate, we need to multiply 'x' to both sides: x*sin(23°) = 8.9
Using a calculator, sin(23°) is 0.39
0.39x = 8.9
By dividing 0.39 to both sides, we should end up with 22.8cm (rounded to the nearest tenth of a centimeter).
