Trigonometry - Worksheet 1.3 Properties of Similar Triangles 1. A forest fire lookout tower casts a shadow 180 ft long at the same time that the shadow of a 9-ft truck is 15 ft long. Find the height of the tower. 2. On a photograph of a triangular piece of land, the lengths of the three sides are 4 cm, 5 cm, and 7 cm, respectively. The shortest side of the actual piece of land is 325 m long. Find the lengths of the other two sides. 3. A lighthouse casts a shadow 28 m long at 7 P.M. At the same time, the shadow of the lighthouse keeper, who is 1.9 m tall, is 3.5 m long. How tall is the lighthouse? 4. A house is 15 ft tall. Its shadow is 40 ft long at the same time the shadow of a nearby building is 300 ft long. Find the height of the building. 5. Assume that Lincoln was 6 1/3 feet tall and his head ¾ ft long. Knowing that the carved head of Lincoln at Mt. Rushmore is 60 ft tall, find how tall his entire body would be if it were carved into the mountain. 6. By drawing lines on a map, a triangle can be formed by the cities of Phoenix, Tucson, and Yuma. On the map, the distance between Phoenix and Tucson is 8 cm, the distance between Phoenix and Yuma is 12 cm, and the distance between Tucson and Yuma is 17 cm. The actual straight-line distance from Phoenix to Yuma is 230 km. Find the distances between the other pairs of cities to the nearest tenth of a kilometer. 7. Before a new car becomes reality, several scale models are built out of clay. On one particular model, a triangular tail light measures 5.3 cm wide by 5.9 cm tall. If the actual tail light is to measure 16.9 cm wide, how tall will it be (to the nearest tenth)? 8. In the early days of modern warfare, the stadia method was commonly applied, as similar triangles could be used to determine the distance to a target (for the artillery). Using a stadiametric range-finding scope, a 2.7-m-tall enemy tank appears to be 1.2 cm tall. If the length of the scope is 56 cm, what is the horizontal distance to the tank? In each diagram, there are two similar triangles. Find the unknown measurement. 9. 11. 10. 12. Find the exact value of the sine, cosine, and tangent of the angle. 13. 30⁰ 14. 45⁰ 15. 60⁰ Find the exact value of the cosecant, secant and cotangent of the angle. 16. 30⁰ 17. 45⁰ 18. 60⁰