If anyone is good at right triangle trig word problems please help
2 answers:
Answer:
- 91 feet
Step-by-step explanation:
<em>Refer to attached picture</em>
Let the base is b and the height of the hill is x.
<u>For the smaller triangle we have:</u>
- x/b = tan 39.3°
<u>And for the bigger triangle: </u>
- (x + 40)/b = tan 49.7°
<u>Solve both equations for b:</u>
- b = x/ tan 39.3°
- b = (x + 40)/tan 49.7°
<u>Eliminate b and get the values of tan, solve for x:</u>
- x/ tan 39.3° = (x + 40) / tan 49.7°
- x tan 49.7° = (x + 40) tan 39.3°
- x( 1.179) = x(0.819) + 40(0.819)
- x(1.179 - 0.819) = 32.76
- x = 32.76/0.36
- x = 91 feet (rounded to the nearest foot)
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