A Tower Casts a Shadow That is 60 Feet Long

3. Find the value of x based on the figures. 8/7 = 10/x 8x = 70 x = 8.75 4. Looking at the triangles in the figure on the right: * a) Are the two triangles similar? Yes * b) What is the length of QT? 9 cm * c) If PR is 15 cm, what is the length of RT? 3 cm 15(4/3) = (x + 4)/9 3x + 12 = 36 3x = 24 x = 8 (h) Find AT x + 1 = 5 + 1 = 6 y/12 = 3/(x + 4) y/12 = 3/(x + 1) 12/16 = 15/(15 + x) 240 = 180 + 12x 60/12 = x 5 = x x/15 = 6/18 18x = 90 x = 5 Math 10 Similar Triangles: Word Problems Name: A statue honoring Ray Hnatyshyn (1934-2002) can be found on Spadina Crescent East, near the University Bridge in Saskatoon. Use the information below to determine the unknown height of the statue.   x/4 = 1.8/2.4 2.4x = 7.2 x = 3 meters A tree 24 feet tall casts a shadow 12 feet long. Brad is 6 feet tall. How long is Brad's shadow? (draw a diagram and solve)   24/12 = 6/x 24x = 72 x = 3 Triangles EFG and QRS are similar. The length of the sides of EFG are 144, 128, and 112. The length of the smallest side of QRS is 280. What is the length of the longest side of QRS? (draw a diagram and solve)   144/x = 198/y = 112/280 112x = 144(280) x = 360 A 40-foot flagpole casts a 5-foot shadow. Find the shadow cast by a nearby building 200 feet tall. (draw a diagram and solve) 40/25 = 200/x 40x = 5000 x = 125 A girl 160 cm tall stands 360 cm from a lamp post at night. Her shadow from the light is 90 cm long. How high is the lamp post?   90/160 = 450/x 90x = 72000 x = 800 cm A tower casts a shadow 7 m long. A vertical stick casts a shadow 0.6 m long. If the stick is 1.2 m high, how high is the tower? (draw a diagram and solve)   x/7 = 1.2/0.6 0.6x = 8.4 x = 14 m Triangles IJK and TUV are similar. The length of the sides of IJK are 40, 50, and 24. The length of the longest side of TUV is 275. What is the perimeter of TUV?   40/x = 50/y = 24/275 50x = 11000 50y = 13750 x = 220 y = 275 Perimeter = 220 + 132 + 275 = 627 A tree with a height of 4 m casts a shadow 15 m long on the ground. How high is another tree that casts a shadow which is 20 m long? (draw a diagram and solve)   4/15 = x/20 15x = 80 x = 16/3 m Triangles CDE and NOP are similar. The perimeter of smaller triangle CDE is 133. The lengths of two corresponding sides on the triangles are 53 and 212. What is the perimeter of NOP?   53/212 = 133/x 53x = 28196 x = 532