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Pre-Calc Exam Notes 5

# Pre-Calc Exam Notes 5 - h 2 8 2 = 17 2 ⇒ h 2 = 289 − 64...

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Angles Section 1.1 5 Example1.3 For each right triangle below, determine the length of the unknown side: A C B 4 a 5 D F E e 1 2 X Z Y 1 1 z Solution: For triangle ABC , the Pythagorean Theorem says that a 2 + 4 2 = 5 2 a 2 = 25 16 = 9 a = 3 . For triangle DEF , the Pythagorean Theorem says that e 2 + 1 2 = 2 2 e 2 = 4 1 = 3 e = radicallow 3 . For triangle XY Z , the Pythagorean Theorem says that 1 2 + 1 2 = z 2 z 2 = 2 z = radicallow 2 . Example1.4 h 8 17 90 A 17 ft ladder leaning against a wall has its foot 8 ft from the base of the wall. At what height is the top of the ladder touching the wall? Solution: Let h be the height at which the ladder touches the wall. We can as- sume that the ground makes a right angle with the wall, as in the picture on the right. Then we see that the ladder, ground, and wall form a right triangle with a hypotenuse of length 17 ft (the length of the ladder) and legs with lengths 8 ft and h ft. So by the Pythagorean Theorem, we have
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Unformatted text preview: h 2 + 8 2 = 17 2 ⇒ h 2 = 289 − 64 = 225 ⇒ h = 15 ft . Exercises For Exercises 1-4, ±nd the numeric value of the indicated angle(s) for the triangle △ ABC . 1. Find B if A = 15 ◦ and C = 50 ◦ . 2. Find C if A = 110 ◦ and B = 31 ◦ . 3. Find A and B if C = 24 ◦ , A = α , and B = 2 α . 4. Find A , B , and C if A = β and B = C = 4 β . For Exercises 5-8, ±nd the numeric value of the indicated angle(s) for the right triangle △ ABC , with C being the right angle. 5. Find B if A = 45 ◦ . 6. Find A and B if A = α and B = 2 α . 7. Find A and B if A = φ and B = φ 2 . 8. Find A and B if A = θ and B = 1/ θ . 9. A car goes 24 miles due north then 7 miles due east. What is the straight distance between the car’s starting point and end point?...
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