Height of Mt. Everest The highest mountain peak in the world is Mt. Everest, located in the Himalayas. The height of this enormous mountain was determined in 1856 by surveyors using trigonometry long before it was first climbed in 1953 . This difficult measurement had to be done from a great distance. At an altitude of
$14,545 \mathrm{ft}$ on a different mountain, the straight-line distance to the peak of Mt. Everest
is $27.0134 \mathrm{mi}$ and its angle of elevation is $\theta=5.82^{\circ} .$ (Source: Dunham, W., The Mathematical Universe, John Wiley and Sons.)
(a) Approximate the height (in feet) of Mt. Everest.
(b) In the actual measurement, Mt. Everest was over $100 \mathrm{mi}$ away and the curvature of Earth had to be taken into account. Would the curvature of Earth make the peak appear taller or shorter than it actually is?