Question

I have no idea what I’m doing.... help please!

Answer 1

Answer:

Step-by-step explanation:

In a 45°, 45°, 90° triangle, Both legs are equal and the hypotenuse is the leg lengths multiplied by the square root of 2.

• Given a triangle with a 45° and 90° angle, the other angle must also be 45°.

• In any of these triangles, the hypotenuse is $\sqrt{2}$ times the side length. You can also find the side length by dividing the hypotenuse by $\sqrt{2}$.

• You can also use this to determine both the legs are the same length. This works the other way too, if both legs are the same length (indicated by a line draw through both sides) the angles opposite to the same length legs are 45°.

In a 30°, 60°, 90° triangle, The hypotenuse is twice the length of the shortest side (the one opposite the 30° angle) and the other leg (the one opposite the 60° angle) is the short leg times $\sqrt{3}$

• If a triangle has two angles out of 30°, 60°, 90°, the last angle must be the only other different angle (because they have to sum to 180)

1. Your answer to the first problem is correct.

2. Because there is a line through two of the sides, they are the same length, and the hypotenuse is $13\sqrt{2}$, the sides are both of length $\frac{13\sqrt{2}}{\sqrt{2}}$ or 13.

3. We can see that there is a 90° angle (from the square in the corner) and a 45° angle. This means that the two legs have equal length. One leg is $4\sqrt{10}$ so the other is the same. The hypotenuse is $4\sqrt{10}  \cdot \sqrt{2}$, or $8\sqrt{5}$

4. The hypotenuse is twice the length opposite the 30° angle (9), so it's length is 18. The last angle must be 60° and the side opposite the 60° must be $9\sqrt{3}$

5. There are two 45, 45, 90 triangle that make up a square. The hypotenuse of both of these is 24, meaning the side lengths are $\frac{24}{\sqrt{2}}$, or, (rationalized), $12\sqrt{2}$

6. 30 60 90 triangle, short side is $\frac{7\sqrt{3}}{\sqrt{3}}$ or 7 and hypotenuse is twice that length, so it is 14.

7. 45 45 90 triangle, hypotenuse is 7 so lengths are $\frac{7}{\sqrt{2}}$ or $\frac{7\sqrt{2}}{2}$

8. 30 60 90 triangle, longer leg is 18, shorter leg is $6\sqrt{3}$, hypotenuse is $12\sqrt{3}$,

9. 45 45 90 triangle, hypotenuse of $3\sqrt{6}$, side lengths of $3\sqrt{3}$

10. 30 60 90, hypotenuse of 28, shorter leg 14, longer leg $14\sqrt{3}$

11. 30 60 90, hypotenuse 15, shorter side $\frac{15}{2}$, longer leg $\frac{15\sqrt{3}}{2}$

12. Two 30 60 90 triangles, hypotenuses of 16, shorter legs of 8 and longer legs of $8\sqrt{3}$