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## 5-5: Solving Right Triangles

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**Alexis Mathis**Aaron Goode Jessica Anderson 5-5: Solving Right Triangles**Pythagorean theorem**• a²+b²=c² • Used to determine the sides of a right triangle**Right triangle basics**• Internal angle=180 • Right angle=90 • The other two angles must add up to 90 • The hypotenuse is the side of the triangle vertical the right angle**Solve triangle ABC given side c = 25 cm and side b = 24**cm. • Solution. To find the remaining side a, use the Pythagorean theorem: • a² + 24² = 25² a² = 625 − 576 = 49 a = = 7. Next, to find angle A, we have • cos A = 2425 = 96100 , on multiplying each term by 4. = .96**inverse**• The arcsine, arccosine, and arctangent of relations**Examples: arcsine**• Sinx=4/9 • X=arcsine4/9 • Sinx=8/24 • X=arcsine8/24**Examples: arccosine**• Cosx=3/4 • X=arccosine3/4 • Cosx=5/7 • X=arccosine5/7**Examples: Arctangent**• Tanx=9/16 • X=arctan9/16 • Tanx=5/11 • X=arctan5/11**Using inverse to solve right triangles**• a=4 • c=6 • SinA=4/6 • A=arcsin4/6**Using inverse..**• b=3 • c=6 • CosA=3/6 • A=arccos3/6**Word problems**• A six-meter-long ladder leans against a building. If the ladder makes an angle of 60° with the ground, how far up the wall does the ladder reach? How far from the wall is the base of the ladder?**Word problems**• A five-meter-long ladder leans against a wall, with the top of the ladder being four meters above the ground. What is the approximate angle that the ladder makes with the ground?