1. Warm-Up!
Find the length of the missing side. Write your answer in simplest radical form.
1.) 4 x
𝒙=𝟒 𝟐 5
5 2 x
2.)
𝒙=𝟓 𝟑
3.) A triangle has side lengths of 9 in, 10 in, and 12 in. Classify the triangle by it’s angles. (HINT: Acute, Obtuse, or Right?)
The triangle would be an acute triangle because 144 < 181.
4.) Joseph has an 8 foot ladder. The ladder reaches up 7 feet on the wall. In order for the ladder to be stable, the base must be less than 4 feet away from the wall. Is Joseph’s ladder stable? Round your answer to the nearest tenth and explain your answer. (HINT: Draw a picture!)
The base of the ladder would be 3.9 feet away so Joseph’s ladder would be safe.

2. Special Right Triangles
Mr. Riddle

3. Triangles
In a triangle, both legs are congruent and the length of the hypotenuse is 2 times the length of the leg.
Hypotenuse = 2 ∙𝐿𝑒𝑔 x
𝑥 2
45°

4. Example 1 – Finding the Length of the Hypotenuse
Find the value of each variable. Leave your answer in simplest radical form.
a.)
b.)
45° x
2 2 9
45° h
ℎ= 2 ∙9
𝒉=𝟗 𝟐
x=2 2 ∙ 2
𝑥=2 4
𝑥=2∙2
𝒙=𝟒

5. YOU TRY!
Find the length of the hypotenuse of a triangle with legs of length
ℎ=5 3 ∙ 2
𝒉=𝟓 𝟔

6. Example 2 – Finding the Length of a Leg
What is the value of x?
𝑥∙ 2 =6
𝑥= 6 2
𝑥= ∙ =
𝒙=𝟑 𝟐
45° x 6

7. You Try!
Find the length of a leg of a triangle with a hypotenuse of length 10.
𝑥∙ 2 =10 𝑥=
𝑥= ∙ =
𝒙=𝟓 𝟐

8. Example 3 – REAL APPLICATION
A high school baseball field is a square. The distance from base to base is 90 feet. To the nearest foot, how far does a catcher throw a ball from home plate to second base.
Since the triangle formed is both isosceles and a right triangle, it must be a triangle. From home to second base would represent the hypotenuse of that triangle.
90 ft
𝒉=𝟗𝟎∗ 𝟐
𝒉=𝟏𝟐𝟕.𝟐𝟕𝟗𝟐𝟐𝟎𝟔
𝒉≈𝟏𝟐𝟕 𝒇𝒆𝒆𝒕

9. You try!
A Softball field has 60 foot base paths. How far does the catcher have to throw from home to second base?
60 ft
𝒉=𝟔𝟎∗ 𝟐
𝒉=𝟖𝟒.𝟖𝟓𝟐𝟖𝟏𝟒
𝒉≈𝟖𝟓 𝒇𝒆𝒆𝒕

10. Triangles
In a Triangle, the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is times the length of the shorter leg.
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒=2∗𝑠ℎ𝑜𝑟𝑡𝑒𝑟 𝑙𝑒𝑔
𝐿𝑜𝑛𝑔𝑒𝑟 𝐿𝑒𝑔= 3 ∗𝑠ℎ𝑜𝑟𝑡𝑒𝑟 𝑙𝑒𝑔 x
𝑥 3 2x
60°
30°

11. Example 4 – Using the length of one side
Find the value of each variable.
5=𝑑 3
𝑑= ∙ = 𝟓 𝟑 𝟑
𝑓=2𝑑
𝑓= = 𝟏𝟎 𝟑 𝟑 d 5 f
60°
30°

12. You Try! Find the value of each variable. 𝑥= 8 2 =𝟒 𝑦=𝑥 3 =𝟒 𝟑 8 x 𝑦
𝑦=𝑥 3 =𝟒 𝟑 x 𝑦 8
60°
30°

13. Homework
ALEKS: Assignment # 40