Question

question 4
1 pts
in a 45 - 45 - 90 triangle, if the hypotenuse measures 15, what is the measure, to the nearest tenth, of the other two sides of the triangles.
15
8.7
10.6
21.2
question 5
1 pts
a tree needs to be staked down before a storm. if the ropes can be tied on the tree trunk 8 feet above the ground and the staked rope should make a 30 degree angle with the ground, how far, to the nearest tenth, from the base of the tree should each rope be staked?
11.3
13.9
4.6
5.7

Explanation:

Step1: Recall the properties of a 45 - 45 - 90 triangle

In a 45 - 45 - 90 triangle, the ratio of the sides is \(1:1:\sqrt{2}\). Let the length of each of the two equal sides be \(x\). The hypotenuse \(c\) is related to the legs \(a = b=x\) by the formula \(c=x\sqrt{2}\).

Step2: Solve for \(x\)

Given \(c = 15\), we have \(x=\frac{c}{\sqrt{2}}\). Rationalizing the denominator, \(x=\frac{15\sqrt{2}}{2}\). Since \(\sqrt{2}\approx1.414\), then \(x=\frac{15\times1.414}{2}=\frac{21.21}{2}=10.605\approx10.6\)

Answer:

C. 10.6