MATH SOLVE

3 months ago

Q:
# GEOMETRY - NEED HELP - WILL MARK BRAINLIESTQUESTION 1An observer is 120 feet from the base of a television tower, which is 150 feet tall. Find the angle of depression at the top of the tower. Round to the nearest degree.QUESTION 2Answer for the image posted below.QUESTION 3What is the opposite of sine called, and what is its triangle ratio?

Accepted Solution

A:

Answer:1) 512) 0.83) cosecantStep-by-step explanation:Question 1The image for this scenario is attached below. Note that base of the television tower forms the side adjacent to the angle and the length of the tower forms the side opposite to the angle. The two angles marked in image are equal because of the property of Alternate Interior Angles.So,Adjacent side = 120 feetOpposite side = 150 feetTangent of an angle is defined as:[tex]tan(\theta)=\frac{Opposite}{Adjacent}[/tex]Using the values, we get:[tex]tan(\theta)=\frac{150}{120}\\\\ tan(\theta)=1.25\\\\ \theta = tan^{-1}(1.25)\\\\ \theta=51.34[/tex]Rounded to the nearest degree, the angle of depression would be 51 degrees.Question 2)We have to find the cosine of angle Z. cos is defined as:[tex]cos(\theta) = \frac{adjacent}{hypotenuse}[/tex]The side adjacent to angle Z is 24 and the hypotenuse is 30. So cos(Z) would be:[tex]cos(Z)=\frac{24}{30}\\\\cos(Z)=0.8[/tex]Therefore, value of cos(Z) for given triangle would be 0.8Question 3The opposite of sine ratio is known as cosecant which is abbreviated as cscSince it is the opposite of sine ratio, it would be calculated as:[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]sine of angle is the ratio of opposite and hypotenuse, so csc would be ratio of hypotenuse to opposite side i.e.[tex]csc(\theta)=\frac{hypotenuse}{opposite}[/tex]