Question

special right triangles (45-45-90)name________ iddate______ block__1)a right triangle with a 45° angle and leg length 82)a right triangle with a 45° angle and hypotenuse length $7sqrt{2}$3)a right triangle with a 45° angle and leg length 44)a right triangle with a 45° angle and leg length 65)a right triangle with a 45° angle and leg length 56)a right triangle with a 45° angle and leg length 137)a right triangle with a 45° angle and leg length $\frac{3sqrt{2}}{2}$8)a right triangle with a 45° angle and leg length $5sqrt{2}$9)a right triangle with a 45° angle and hypotenuse length 210)a right triangle with a 45° angle and leg length $\frac{13sqrt{2}}{2}$11)a right triangle with a 45° angle and leg length $3sqrt{3}$12)a right triangle with a 45° angle and leg length 12

Explanation:

For 45-45-90 triangles:

• If leg length = $a$, hypotenuse = $a\sqrt{2}$
• If hypotenuse = $c$, leg length = $\frac{c}{\sqrt{2}} = \frac{c\sqrt{2}}{2}$

1) Find missing hypotenuse

Leg = 8, hypotenuse = $8\sqrt{2}$

2) Find missing leg

Hypotenuse = $7\sqrt{2}$, leg = $\frac{7\sqrt{2}}{\sqrt{2}} = 7$

3) Verify hypotenuse

Leg = 4, hypotenuse = $4\sqrt{2}$

4) Find missing hypotenuse

Leg = 6, hypotenuse = $6\sqrt{2}$

5) Verify hypotenuse

Leg = 5, hypotenuse = $5\sqrt{2}$

6) Verify hypotenuse

Leg = 13, hypotenuse = $13\sqrt{2}$

7) Find missing legs

Hypotenuse = $\frac{3\sqrt{2}}{2}$, leg = $\frac{\frac{3\sqrt{2}}{2}}{\sqrt{2}} = \frac{3}{2}$

8) Verify sides

Leg = $5\sqrt{2}$, other leg = $5\sqrt{2}$, hypotenuse = $5\sqrt{2} \times \sqrt{2} = 10$

9) Find missing legs

Hypotenuse = 2, leg = $\frac{2}{\sqrt{2}} = \sqrt{2}$

10) Find missing hypotenuse

Leg = $\frac{13\sqrt{2}}{2}$, hypotenuse = $\frac{13\sqrt{2}}{2} \times \sqrt{2} = 13$

11) Find missing legs

Hypotenuse = $3\sqrt{3}$, leg = $\frac{3\sqrt{3}}{\sqrt{2}} = \frac{3\sqrt{6}}{2}$

12) Verify hypotenuse

Leg = 12, hypotenuse = $12\sqrt{2}$

Answer:

1. $\boldsymbol{8\sqrt{2}}$
2. $\boldsymbol{7}$
3. $\boldsymbol{4\sqrt{2}}$ (correct as written)
4. $\boldsymbol{6\sqrt{2}}$ (correct as written)
5. $\boldsymbol{5\sqrt{2}}$ (correct as written)
6. $\boldsymbol{13\sqrt{2}}$ (correct as written)
7. $\boldsymbol{\frac{3}{2}}$ (both legs)
8. Other leg: $\boldsymbol{5\sqrt{2}}$, Hypotenuse: $\boldsymbol{10}$
9. $\boldsymbol{\sqrt{2}}$ (both legs)
10. $\boldsymbol{13}$
11. $\boldsymbol{\frac{3\sqrt{6}}{2}}$ (both legs)
12. $\boldsymbol{12\sqrt{2}}$ (correct as written)