Section 7 – 3 Special Right Triangles

Objectives:To use the properties of 45-45-90

trianglesTo use the properties of 30-60-90

triangles

45-45-90 TrianglesSolve for y in terms of x.

45-45-90 Triangle Theorem

In a 45-45-90 triangle, both legs are congruent and the length of the hypotenuse

is times the length of a leg.

𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆=√𝟐 ∙ 𝒍𝒆𝒈

𝒍𝒆𝒈=𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆

√𝟐

Example 1 Finding the Length of the Hypotenuse

Find the value of each variable.

A) B)

C) Find the length of the hypotenuse of a 45-45-90 triangle with legs of length

D) Find the length of the hypotenuse of a 45-45-90 triangle with legs of length

Example 2 Finding the Length of a Leg

Find the value of x.

A) B)

C) Find the length of a leg of a 45-45-90 triangle with a hypotenuse of length 10.

D) Find the length of a leg of a 45-45-90 triangle with a hypotenuse of length 22.

Example 3 Real-World Connection

A) A square garden has sides 100 feet long. You want to build a brick path along a diagonal of the square. How long will the path be? Round your answer to the nearest foot.

B) The distance from one corner to the opposite corner of a square playground is 96 feet. To the nearest foot, how long is each side of the playground?

C) You are designing dinnerware. What is the length of a side of the smallest square plate on which a 20-cm chopstick can fit along a diagonals without any overhang?

Textbook Page 369; # 1 – 11 Odd

Section 7 – 3 Continued…

Objectives:To use the properties of 30-60-90 triangles

30-60-90 TrianglesLabel the sides of the triangle as

HYPOTENUSE, LONG LEG, or SHORT LEG.

30-60-90 Triangle Theorem

In a 30-60-90 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 ∙𝒔𝒉𝒐𝒓𝒕 𝒍𝒆𝒈

𝒍𝒐𝒏𝒈𝒍𝒆𝒈=√𝟑∙ 𝒔𝒉𝒐𝒓𝒕 𝒍𝒆𝒈

Example 4 Finding the Lengths of the Legs

Find the value of each variable. Leave your answers in simplest radical form.

A) B)

C) Find the lengths of the legs of a 30-60-90 triangle with hypotenuse of length 12.

D) Find the lengths of the legs of a 30-60-90 triangle with hypotenuse of length .

Example 5 Using the Length of a Leg

Find the value of each variable. Leave your answers in simplest radical form.

A)

B)

C) The shorter leg of a 30-60-90 triangle has length . What are the lengths of the other two sides?

D) The longer side of a 30-60-90 triangle has length 18. Find the lengths of the shorter leg and the hypotenuse.

Homework:7 – 3 Ditto; 1 – 13

Section 7 – 3 Continued…

Objectives:To use the properties of 45-45-90 & 30-60-

90 triangles

Example 6 Multi-Step Problems

A) The deer warning sign is an equilateral triangle. Each side is 1 meter long. Find the area of the sign.

B) A rhombus has 10-inch sides, two of which meet to form a 30 degree angle. Find the area of the rhombus.

C) A rhombus has 10-inch sides, two of which meet to form a 60 degree angle. Find the area of the rhombus.

D) E)

Find the value of each variable. Leave your answer in simplest radical form.

F) G)

Find the area of each figure. Round to the nearest tenth.

HomeworkTextbook Page 370 – 371; #25, 26, 27, 29, 34, 36, 38 , 39