The path between three landmarks in a national park form a right triangle. The oldest living evergreen tree is at point A, the
ranger station is at point B, and the natural hotspring is at point C. The right angle is at point C, and there is a 60degrees angle at point B. If the distance between the hotspring and the evergreen tree is 601 yards, find the distance, x, from the hotspring to the ranger station.
1 answer:
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1. Angle PAB is 90 degrees, as it is formed from the tanget to the circle at A, and the radius drawn to A.
2. AB=BC, because tangents drawn to a circle from the same point are equal.
3. PB is Common, so by the side-side-side congruence postulate, triangles ABP and CBP are congruent.
4. So measure of m(BPA)=x/2 and m(ABP)=73/2.
5.
, x= 107 degrees.
2. AB=BC, because tangents drawn to a circle from the same point are equal.
3. PB is Common, so by the side-side-side congruence postulate, triangles ABP and CBP are congruent.
4. So measure of m(BPA)=x/2 and m(ABP)=73/2.
5.