Question

a balloon is 50m high its angle of elevation from observer A is 45 and from observer B it is 30 what is the distance between observer b and observer a from the baloon

Answer 1

$$x=\dfrac{h}{\tan\theta}$$

$$x_A=\dfrac{50}{\tan45\degree}=50(m)$$

$$x_B=\dfrac{50}{\tan30\degree}=50\sqrt{3}(m)$$

Maximum distance

$$d_{max}=x_A+x_B=50+50\sqrt{3}=50(1+\sqrt{3})(m)$$

$$\approx136.6(m)$$

Minimum distance

$$d_{max}=-x_A+x_B=-50+50\sqrt{3}=50(\sqrt{3}-1)(m)$$

$$\approx36.6(m)$$