Phoebe and Tucker are 48m apart. Phoebe looks up at an angle of 43 degrees to see a hot air balloon hovering in the sky directly between her and Tucker. Tucker looks up at an angle of 31 degrees to see the hot air balloon.
A.) Explain how it could be determined who is closer to the balloon without doing any calculations.
B.) Determine the distance between the balloon and the person nearest the balloon. (I think I have to use sine but I'm not sure how to do this.)

  1. 👍
  2. 👎
  3. 👁
  1. Make a sketch, with P for Phoebe and T for Tucker as a horizontal line, so that PT = 45 m
    Let B be the position of the balloon, so that angle BPT = 43° and angle BTP = 31°
    Let AB be the height of the balloon with A directly below B on PT

    sin 43° = AB/BP ---> BP = AB/sin43
    sin 31° = AB/BT ---> BT = AB/sin31
    now we know, or should know, that sin 43>sin31
    So AB divided by the larger number would produce the smaller answer.
    So BP < BT
    (notice I did not do any calculations)

    To actually find PB, let PA = x, the AT = 48-x
    tan 43 = AB/x
    AB = xtan43

    tan31 = AB/(48-x)
    AB = (48-x)tan31

    so xtan43 = 48-xtan31
    xtan43 + tan31 = 48
    x(tan43+tan31) = 48
    x = 48/(tan43+tan31)

    now cos 43 = x/BP
    BP = x/cos43
    = (48/(tan43 + tan31) )(1/cos43)
    only now do we do any calculation ....

    I get BP = 42.8 m

    check my work please

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. geometry

    Two lines intersect at a point. The vertical angles formed are supplementary. What is the measure of each of the angles? So my question is if both angle 1 and 2 must equal 90 degrees each? Im wondering because I know that angle 1

  2. Math

    Which of the following values best approximates of the length of c in triangle ABC where c = 90(degrees), b = 12, and B = 15(degrees)? c = 3.1058 c = 12.4233 c = 44.7846 c = 46.3644 In triangle ABC, find b, to the nearest degree,

  3. algebra

    The sum of the angles of a triangle is 180 degrees. If one angle measures x degrees, a second angle measures 3x degrees, and a third angle measures 7x degrees, express the measure of the fourth angle in terms of x.

  4. Math

    The measure of angle BCA is: A) 30 degrees B) 36 degrees C) 45 degrees D) 60 degrees It is a iscoles triangle which the number 3x on the top of the triangle angle A and a line extending to D going right from A and Angle B is at

  1. ELA

    What are the differences and similarities between Sal And Phoebe???

  2. Math

    One angle of an isosceles triangle is 28°. What are the other 2 angles? (Choose all that apply.) 76 degrees and 76 degrees 116 degrees and 116 degrees 28 degrees and 152 degrees 28 degrees and 124 degrees

  3. Geometry

    Angle A and Angle B are complementary andgles and the m Angle A = 58 degrees, what is he measure of the supplement of Angle B. This is what I did Angle A and Angle B = 90 degrees, mAngle A = 58 degrees 90 - 58 = 32 degrees 180 -

  4. math

    i need help on unit 1 lesson 10 Geometry unit test. Name a pair of complementary angle.

  1. Math

    Phoebe wen to a pet shop and saw birds and puppies. There are 18 animals in all in the pet shop. If Phoebe saw 50 animal legs on all, how many puppies and how many birds are there in the pet shop?

  2. geometry

    Prove that if angle DAC is 40 degrees and angle ACD is 35 degrees, then angle BDA is 70 degrees. Write a two column proof showing statements and reasons. My teacher said my answer was wrong because BCA cannot equal 40 degrees

  3. Math

    ABCD is a kite with AD=AB Angle A is 116 degrees Angle B is 2x degrees Angle D is (5x-147) degrees Find the smallest angle of the kite

  4. trigonometry

    A wheel with a 20-inch radius is marked at two points on the rim. The distance between the marks along the wheel is found to be 3 inches. What is the angle (to the nearest tenth of a degree) between the radii to the two marks?

You can view more similar questions or ask a new question.