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Section 5-5: Solving Right Triangles

Section 5-5: Solving Right Triangles. Your calculator can find sine, cosine, and tangent in degrees and radians. sin cos tan We will use their definition to find secant, cosecant, and cotangent .

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Section 5-5: Solving Right Triangles

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  1. Section 5-5: Solving Right Triangles • Your calculator can find sine, cosine, and tangent in degrees and radians. • sin cos tan • We will use their definition to find secant, cosecant, and cotangent. • csc= sec = cot = • When using the calculator, first you must determine if the angle is in DEGREES or RADIANS. Put your calculator in the appropriate MODE. • Example 1: Use the calculator to find the following. • a) cot 45° b) csc 30° c) sec 22.5° • INVERSE OF THE SINE, COSINE AND TANGENT FUNCTIONS • How do we solve : sin = -.5 = = -30

  2. That means, sin-1 and sin will cancel each other out, as well as cosand cos-1, or tan and tan-1. We go backward on the calculator to find the angle in degrees or radians using the sin-1called arcsinecos-1called arccosine tan-1 called arctangent Arcsine, arccosine and arctangent are ____________not functions. When going backward, the best method for understanding your key sequence on the calculator is to solve algebraically for first, then type into the calculator. Example 2: Find in degrees. a) cos b) sin = .7216 c) tan = 1.1256 relations = = = 46.18673788 = 60 = 48.38162965 46.2

  3. Example 1: If r = 14 and s = 8, find S. You want to find the measure of an acute angle in a right triangle. You know the side opposite the angle and the hypotenuse. Angle S is about 34.8 S = 34.8499

  4. Trigonometry can be used to find the angle of ______________ or the angle of depression. Example 2: HOUSEHOLDThe camera for a baby monitor is set up on a shelf in a child’s room, and it is angled so that it captures the image of the center of the baby’s crib. The shelf is about 3 feet higher than the crib, and its horizontal distance from the crib is about 7 feet. What is the angle of depression of the light? The angle of depression and the angle of elevation are equal in measure because they are alternate interior angles. The angle of depression should be about 23.2

  5. You can use trigonometric functions and inverse relations to solve right triangles. To solve a right triangle means to find __________________________ and ____________. all the measures of its sides the angles *** Whenever possible, use the measures given in the problem to find the unknown measures. Example 3: Solve each triangle described, given the triangle at the right. A.B = 42°, b = 4.5 Find A : A + 42 + 90= 180 A = 48 Find a : tan 48 Find c : cos a = 4.9978 c = 6.7251

  6. B. b= 18, c = 52 Find a : a2 + (18)2 = (52)2 a2 + 324 = 2704 a2 = 2380 a = Find A : A = A = 69.7948 A = Find B : 69.8 B = 20.2

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