Exercise 25 Page 765

Notice that the lines from the satellite are tangent to the Earth. Let's mark the corresponding tangency points.

Since the lines tangent to the circle intersect each other outside the circle, we have that m∠ ASB is equal to one half the measure of the difference of the intercepted arcs. m∠ ASB = 1/2(m AB - x^(∘)) Notice that we do not know the measure of the major arc AB. However, we can write it in terms of the measure of the minor arc. m AB + x^(∘) = 360^(∘) ⇓ m AB = 360^(∘) - x^(∘) Additionally, we are told that m∠ ASB = 12^(∘). Thus, we are ready to find the measure of the planet's arc visible to the satellite.

m∠ ASB = 1/2(m AB - x^(∘))

SubstituteII

m AB= 360^(∘) - x^(∘), m∠ ASB= 12^(∘)

12^(∘) = 1/2( 360^(∘) - x^(∘) - x^(∘))

▼

Solve for x^(∘)

SubTerms

Subtract terms

12^(∘) = 1/2(360^(∘) - 2 x^(∘))

MultEqn

LHS * 2=RHS* 2

24^(∘) = 360^(∘) - 2 x^(∘)

SubEqn

LHS-360^(∘)=RHS-360^(∘)

-336^(∘) = -2 x^(∘)

DivEqn

.LHS /-2.=.RHS /-2.

168^(∘) = x^(∘)

RearrangeEqn

Rearrange equation

x^(∘) = 168^(∘)