What we know so far: Side 1 = 55m Side 2 = 65m Angle 1 = 40° Angle 2 = 30°
What we are looking for: Toby's Angle = ? The distance x = ?
We need to look for Toby's angle so that we can solve for the distance x by assuming that the whole figure is a SAS (Side Angle Side) triangle.
Solving for Toby's Angle: We know for a fact that the sum of all the angles of a triangle is 180°; therefore, 180° - (Side 1 + Side 2) = Toby's Angle Toby's Angle = 180° - (40° + 30°) Toby's Angle = 110°
Since we already have Toby's angle, we can now solve for the distance x by using the law of cosines r² = p²+ q²<span>− 2pq cos R where r is x, p is Side1, q is Side2, and R is Toby's Angle. </span> x² = Side1² + Side2² - 2[(Side1)(Side2)] cos(Toby's Angle) x² = 55² + 65² - 2[(55)(65)] cos(110°) x² = 3025 + 4225 -7150[cos(110°)] x² = 7250 - 2445.44 x = √4804.56 x = 69.31m
