a Start by finding the length of the legs of the smaller triangle.
B
b Find the difference between the length of the longer leg of the larger triangle and the length of a leg of the smaller triangle.
A
a 8.5 meters
B
b 3.1 meters
Practice makes perfect
a Let's start by finding the length of the legs of the smaller triangle. Then we will use this to find the length of the longer brace. The smaller triangle is a 45 ° -45° -90° triangle.
In a 45 ° -45° -90° triangle, both legs are congruent and the length of the hypotenuse is sqrt(2) times the length of a leg.
Hypotenuse= sqrt(2) * Leg
⇕
6 m= sqrt(2) * Leg
Let's solve this equation for the length of each leg.
Now we can look at the larger triangle, which is a 30 ° -60 ° -90 ° triangle. In a 30 ° -60 ° -90 ° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is sqrt(3) times the length of the shorter leg. Let's look at the given triangle.
In a 30 ° -60 ° -90 ° triangle, the shorter leg will be opposite the 30 ° angle. The leg of the smaller triangle we found above is the same as the shorter leg of the larger triangle. Therefore, the hypotenuse will be twice the length of the shorter leg, 3 sqrt(2) meters.
The longer brace is approximately 8.5 meters long.
b The distance between the highest point of the longer brace and the highest point of the shorter brace will be the difference of their leg lengths. We have already found the length of the legs for the smaller triangle. However, we must solve for the length of the longer leg of the larger triangle.
Finally, we will take the difference between the length of the longer leg of the large triangle and the length of the leg of the smaller triangle.
Distance between Braces=Longer Leg-Shorter Leg
⇕
Distance between Braces=3 sqrt(6)-3 sqrt(2) ≈ 3.1 m
The longer brace reaches about 3.1 meters higher than the shorter brace.
