warm up. essential question how can i solve for side lengths of a right triangle and how can you use...
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Warm UP
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Essential Question
How can I solve for side lengths of a right triangle and how can you use side lengths to determine whether a triangle is acute, right, or obtuse?
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Lesson 41 Unit 2: Right Triangles
Section 1: The Pythagorean Theorem
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Standard(s):
MCC9-12.G.SRT.8Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
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Pythagorean theorem
- The theorem states that in a right triangle , the sum of the squares of the lengths of the legs equals the square of the hypotenuse.
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NOTE:
• The hypotenuse is always directly across from the 90 degree angle
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We can use the Pythagorean theorem to solve for a missing side length in right triangles
Find the missing variable:1.A = 6, B= 9, C = ?2.A = 4, B = ? C = 113.A = ? B = 4, C = 134.A = 2, B = 13, C = ?5.A =7, B = ? C = 14
A
B
C
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Application ProblemTo prevent a ladder from shifting, safety experts
recommend that the ratio of h:d be 4:1. How far from the base of the wall should you place the foot of a 10- foot ladder? Round to the nearest inch.
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Solution
Based on the picture and what we know aboutThe Pythagorean theorem: D2 + h2 = l 2
We also know l = 10 because the Ladder is 10 feet tall
Let d have length x. Based on the ratio, h = 4x
So, (x)2 + (4x)2 = (10)2
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Pythagorean triple
• A set of 3 nonzero whole numbers a, b, and c such that a2 + b2 = c2.
- The largest side length is the hypotenuse
Some common Pythagorean triples are: 3,4,55,12,138,15,177,24,25
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Find the missing side length and Identify if the following is a Pythagorean triple
15
12
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Find the missing side length and Identify if the following is a Pythagorean triple
15
9
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In order to have a triangle
The two smaller side lengths added together must be larger than the largest side length
If they aren’t the sides can’t touch
17
1
7
17
15
8
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Different kinds of trianglesRight triangles
angle C = 90 degrees c2 = a2 + b2 Obtuse triangles
Angle C > 90 degreesc2 > a2 + b2
Acute triangles angle C < 90 degrees
c2 < a2 + b2 Note: c is the longest side of the triangle
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Tell if the measures can be the side lengths of a triangle. If so, Classify the triangle as acute, obtuse, or right
a. 8,11,13
b. 5.8, 9.3, 15.6