Need fast! a scientist is trying to measure the distance across a marsh as shown in the figure above. he chooses two points at either end of the marsh representing the endpoints of the desired distance, d. he then chooses another point away from the marsh's border so that a right triangle is formed. he calculates that the angle between the base of this triangle and its hypotenuse is 45° . he then measures one of the sides of the triangle to be 300 m. what is the length, d, across the marsh? round to the nearest tenth of a mete

That is a 45 45 90 triangle.The hypotenuse of such a triangle equals one of the legs multiplied by the square root of 2.300 * sq root (2)=300 * 1.4142135624 Distance "D" = 300 * 1.4142135624 Distance "D" = 424.3 meters
(rounded to the nearest 10th of a meter.

Source:http://www.1728.org/trig2.htm

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12