Right Triangles and Trigonometry

SAT Math· difficulty 5/5

From points AA and BB on level ground, 4040 ft apart, the angles of elevation to the top of a tower are 45°45° and 60°60° respectively, with BB closer. What is the height of the tower? (Approximate to nearest ft using 31.732\sqrt{3}\approx 1.732.)

  • A

    6060

  • B

    9595

    check_circle
  • C

    7373

  • D

    5555

Explanation

Let height =h=h, distance from BB to base =d=d. Then h=dtan60°=d3h=d\tan 60°=d\sqrt{3} and h=(d+40)tan45°=d+40h=(d+40)\tan 45°=d+40. So d3=d+40d\sqrt{3}=d+40, d(31)=40d(\sqrt{3}-1)=40, d54.6d\approx 54.6, h94.695h\approx 94.6\approx 95.

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