Ask questions and get helpful answers.

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. 👁
  4. ℹ️
  5. 🚩
1 answer
  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. 👎
    3. ℹ️
    4. 🚩

Answer this Question

Similar Questions

  1. PHYSICS

    A FIREWORKS ROCKET IS MOVING WITH A SPEED OF 45.0 M/S. THE ROCKET SUDDENLY BREAKS INTO TWO PIECES OF EQUAL MASS, WHICH FLY OFF WITH VELOCITIES V1 AND V2. WHAT IS THE MAGNITUDE OF V1? (THE ANGLE OF V1 WITH RESPECT TO THE ORIGINAL V DIRECTION IS 30 DEGREES

  2. math

    Altitudes AD and BE of acute triangle ABC intersect at point H. If angle AHB = 123 degrees and angle BAH = 26 degrees, then what is angle HCA in degrees? Asymptote code below [asy] size(150); defaultpen(linewidth(0.8)); pair B = (0,0), C = (3,0), A =

  3. mathematics

    For each of the following, tell how many non congruent triangles PQR fit the given description, and find the size of angle Q. Make a separate diagram for each case. (a) p = 3, q = 5, angle P = 27 degrees (b) p = 8, q = 5, angle P = 57 degrees (c) p = 7, q

  4. Unit 2 Lesson 4 math 6B school year 2021-2022

    Unit 2 Lesson 4, Types of Triangles Practice, math 6B, school year 2021-2022 answers. Only use this to check your work: 1. Select the correct classification for the triangle shown below. Answer: isosceles Explanation: This triangle is an isosceles triangle

  5. Math,geometry

    Point $P$ is on side $\overline{AC}$ of triangle $ABC$ such that $\angle APB =\angle ABP$, and $\angle ABC - \angle ACB = 39^\circ$. Find $\angle PBC$ in degrees.

  6. Math

    The measure of one base angle in an isosceles triangle is 20 degrees. The measure of the largest angle in the triangle is A) 20 degrees B) 90 degrees C) 140 degrees D) 160 degrees

  7. MATH_URGENT

    Point X is on side \overline{AC} of \triangle ABC such that \angle AXB =\angle ABX, and \angle ABC - \angle ACB = 39 degrees. Find \angle XBC in degrees.

  8. Math

    Four of the angles of a pentagon measure 85 degrees, 110 degrees, 135 degrees, and 95 degrees. Find the measure of the missing angle. A. 115 degrees B. 95 degrees C. 135 degrees D. 85 degrees Is the answer D?

  9. Physics

    An archer standing on a cliff 48m above the level field below shoots an arrow at an angle of 30° above the horizontal with a speed of 80m/s. How far from the base of the cliff will the arrow land?

  10. samoana high school

    phoebe physics pulls a wagon with a force of 80 N. a) what is the net force of friction between the wagon and the ground is 12 N. b) if she uses 80 N to pull the wagon through a med puddle, and the net force on the wagon is 38 N, what friction force asts

Still need help?

You can ask a new question or browse existing questions.