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WARM UP

WARM UP. 1. Find the area of a triangle with sides 102 cm, 36 cm and 110 cm. Lesson 20 -Advanced Problems. Objective: To solve any problem involving a triangle. Solving Advanced Problems. Read the problem carefully. Draw a diagram Is it a right triangle? SOHCAHTOA Inverse functions

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WARM UP

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  1. WARM UP • 1. Find the area of a triangle with sides 102 cm, 36 cm and 110 cm.

  2. Lesson 20 -Advanced Problems Objective: To solve any problem involving a triangle.

  3. Solving Advanced Problems • Read the problem carefully. • Draw a diagram • Is it a right triangle? • SOHCAHTOA • Inverse functions • Is it an oblique triangle? • Law of Sines • Law of Cosines

  4. Example (p195) • Suppose that everyone in town knows that a 30-foot-tall steeple has been built on top of a particularly large church. When you go to look at it, you notice that the tip of the steeple is 38o above the horizontal while the base of the steeple is 32o above the horizontal. How tall is the church together with the steeple? 30 ft. x

  5. A pole stands 49 feet tall on a hill. The distance from the top of the pole to the end of the shadow is 31 feet, and the angle at the top of the pole is 20° (in the picture). What is the length of the shadow?

  6. Since we don't have a side and angle that are opposite each other, let's use the Law of Cosines:a2 = b2 + c2 - 2bc cos AFilling in values, we get:a2 = 492 + 312 - 2(49)(31) cos 20°a2 = 507.2138181a = 22.52 feet

  7. Finding the Area of a Polygon • Sum of the angles of a regular polygon = (n-2)180 = 540o. • Each angle = 540/5 = 108o 4 in 2 in The angle in this right triangle is 54o Now use trig to find the height of the triangle. Area of the triangle = ½(2)(2.75)= 2.75. 10 triangles = 27.5 in2

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