Will mark
a surveyor is “shooting a line” to a point on a tree 70 m from his current position. after rotating his surveying instrument 25° to the left, he “shoots” another line to a point on a fence post 35 m away. determine the distance between the point on the tree to the point on the fence post. (do not assume that the triangle shown is a right triangle) show all work. round answer to the nearest hundredths.
use the law of sines to find the measure of
find the measure of

41.04 meters

Step-by-step explanation:

The questions which involve calculating the angles and the sides of a triangle either require the sine rule or the cosine rule. In this question, the two sides that are given are adjacent to each other the given angle is the included angle. The initial position is given by A. The tree is denoted as C and the fence post is denoted as B. Since the use of sine rule will complicate the question, it will be easier to solve this question using the cosine rule. Therefore, cosine rule will be used to calculate the length of BC. The cosine rule is:

BC^2 = AB^2 + AC^2 - 2*AB*AC*cos(BAC).

The question specifies that AC = 70 meters, BAC = 25°, and AB = 35 meters. Plugging in the values:

BC^2 = 35^2 + 70^2 - 2(35)(70)*cos(25°).

Simplifying gives:

BC^2 = 1684.091844.

Taking square root on the both sides gives BC = 41.04 meters (rounded to two decimal places).

Therefore, the distance between the point on the tree to the point on the fence post is 41.04 meters!!!

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