a Where is the intersection point of the lines of sight? According to its position, use the corresponding formula.
B
b Where is the intersection point of the lines of sight? According to its position, use the corresponding formula.
A
a 145^(∘)
B
b 30^(∘)
Practice makes perfect
a In the given diagram, let's mark the tangency points between the line of sight of the camera and the carousel.
We are told that the camera's viewing angle is 35^(∘) — that is, m∠ACB = 35^(∘). Our mission is to find the measure of AB. To do it, we use the fact that the tangent lines AC and BC intersect each other outside the circle (carousel). This leads us to the following formula.
m∠C = 1/2(mADB - mAB)
Next, let's write the major arc in terms of the minor arc.
mADB + mAB = 360^(∘)
⇓
mADB = 360^(∘) - mAB
Finally, let's substitute this expression and the measure of the viewing angle into the formula written above.
b In this part, we want to find the measure of the viewing angle such that the arc measure captured by the camera is 150^(∘).
As before, by using the fact that CA and CB are tangent to the circle and they intersect each other outside the circle, we establish the following equation.
m∠C = 1/2(mADB - m AB)
Since the sum of the measures of the arcs equals 360^(∘), we can find the measure of the major arc.
mADB + m AB^(150^(∘)) = 360^(∘)
⇓
mADB = 210^(∘)
Finally, let's substitute the corresponding measures to find the measure of the viewing angle the photographer should use.
