1.6 Law of (co)sine practice 3

(Calculator) Solve the triangle by finding all remaining side lengths and angle measures. If there is no triangle that satisfies the given conditions, type “0” in each blank. If there is more than one triangle that is consistent with the given conditions, write the triangle that satisfies [math]c[/math] is the longest side.
Note: round your answers to nearest integers.

(a) [math]A=30^{\circ}, b=12, a=10[/math]

(b) [math]B=125^{\circ}, b=10, c=12[/math]

(Calculator) A fugitive in a car is travelling across the Bonneville Salt Flats (of land speed records fame) in Utah. He leaves the road at an angle of [math]N60 ^{\circ}W[/math] and drives straight in a straight line at [math]140 km/h [/math]. At the moment he leaves the road, the police officer is pursuing him is exactly 100 m behind him. She leaves the road at an angle of [math]N45^{\circ}W[/math] intending to intercept his car. How far will each car travel to reach the point where their two paths meets? (1 decimal place)

(Calculator) Given the measurements below, determine how many triangles are possible.

(a) [math]A=40^{\circ}, a=15, c=12[/math]

(b) [math]B=55^{\circ}, b=10, a=12[/math]

(c) [math]a=3, b=4, c=8[/math]

(d) [math]A=114^{\circ}, a=11, c=8[/math]

(Calculator) Two ships leave a harbor, one travelling at 40 km/hr and the other at 35 km/hr. If the two ships are traveling on courses that have an angle of [math]140 ^{\circ}[/math] between them, how far apart are the ships (in km) after 6 hours. Round to nearest integer.

(Calculator) Find the angle [math]Q[/math] of [math]\Delta PQR[/math] if [math]p=7, q=10[/math], and [math]r=5[/math]. (one decimal place)

(Calculator) Find the area of quadrilateral [math]ABCD[/math].

(Calculator) A plane flies a straight course. On the ground directly below the flight path, observes 2 miles apart spot the plane at the same time. The plane’s angle of elevation is [math]46^\circ[/math] from one observation point and [math]71^\circ[/math] from the other. How high is the plane?

(Calculator) Consider a triangle [math]ABC[/math] where [math]a=8[/math]cm, [math]b=14[/math]cm, and [math]c=10.2[/math]cm. Round your answer to nearest hundredth.

(a) Find [math]m\angle A, m\angle B[/math] and [math]m\angle C[/math].

(b) Find the area, in [math]\text{cm}^2[/math], of triangle [math]ABC[/math] using Heron’s formula.

(Calculator) Consider a triangle [math]ABC[/math] with [math]m\angle A=67^\circ[/math], [math]a=17[/math]cm and [math]b=14[/math]cm. Find [math]c[/math]. If you have two answers, write the biggest one.

(Calculator) Consider a triangle [math]ABC[/math] with [math]m\angle A=47^\circ[/math], [math]a=14[/math]cm and [math]b=17[/math]cm. Find [math]c[math]. Round your answer to nearest hundredth. If you have two answers, write the smallest one.