Wording of a Trigonometry Problem

[Bardagath]

Hi,

This is a problem that has been very confusing for me and I feel it could be because I am misinterpreting the wording:

A tree standing (vertically) on a slope inclined at an angle of 11° to the horizontal casts a shadow of length 15m up the slope. If the angle of elevation of the sun is 72.5°, how high is the tree?

From what I interpret from this, I imagine a horizontal line connected to another line (which is inclined at 11°). I make a vertical line perpendicular to the horizontal line which passes through the incline and this represents a tree. I then draw another line passing through the vertical line which connects at an angle of 72.5° (Angle A) to the incline. The line AB is 15 units in length and is labeled as side c of our triangle, which is opposite angle C.

I consider the "tree" and the horizontal perpendicular at 90° to each other. Therefore I reason that 90°-11°=79° which is correct when deducing this from a geometric drawing. I use this for determining Angle B of our subject triangle and subtracting Angles A and B from 180, determine angle C. We now calculate the length of the "tree" (line AB) using the sine rule.


Is my interpretation of the wording of this problem correct or am I constructing the wrong triangle? My answer for the side A of the triangle, the "tree", is 29.98 but according to my study guide the side A is 49.56. What are the errors in my analysis?

 

[hamster143]

The error is that the angle A is not 72.5°. 72.5° is the angle between the line AC and the horizontal. The angle between AC and the incline is 72.5° + 11°.

 

[Bardagath]

Thanks hamster143,

So the problem is that I misinterpreted the wording of the problem. Should angles of elevation always be measured from a horizontal? Why would you not measure the angle of elevation to the sun from the incline?

The key word here is "angle of elevation"? ( Defined as always measured from a horizontal? )

 

[hamster143]

Precisely. Angle of elevation is by definition always measured from the horizontal plane. Besides, it would be illogical to measure elevation of the Sun or any other celestial object with respect to local topographic features rather than the horizon.