91Ó°ÊÓ

A triangle has sides of lengths 10 \(\mathrm{cm}\) and \(16 \mathrm{cm},\) and the measure of the angle between them is \(130^{\circ} .\) Find the area of the triangle.

In \(\triangle D E F, d=15\) in, \(e=18\) in., and \(f=10\) in. Find \(m \angle F\)

Use a calculator and inverse functions to find the radian measures of the angles. angles whose cosine is 0.58

Given \(\cos \theta=-\frac{15}{17}\) and \(180^{\circ}<\theta<270^{\circ}\) , find the exact value of each expression. $$ \cos \frac{\theta}{2} $$

Forestry A forest ranger in an observation tower sights a fire \(39^{\circ}\) east of north. A ranger in a tower 10 miles due east of the first tower sights the fire at \(42^{\circ}\) west of north. How far is the fire from each tower?

Geometry The sides of a triangle are 15 in., 17 in., and 16 in. long. The smallest angle has a measure of \(54^{\circ} .\) Find the measure of the largest angle. Round your answer to the nearest degree.

Navigation A pilot is flying from city \(A\) to city \(B,\) which is 85 mi due north. After flying 20 \(\mathrm{mi}\) , the pilot must change course and fly \(10^{\circ}\) east of north to avoid a cloudbank. a. If the pilot remains on this course for \(20 \mathrm{mi},\) how far will the plane be from city \(\mathrm{B} ?\) b. How many degrees will the pilot have to turn to the left to fly directly to city B? How many degrees from due north is this course?

In \(\triangle A B C, m \angle A=40^{\circ}\) and \(m \angle B=30^{\circ} .\) Find each value to the nearest tenth. Find \(B C\) for \(A B=5.9 \mathrm{cm}\)

Sailing Buoys are located in the sea at points \(A, B,\) and \(C . \angle A C B\) is a right angle. \(A C=3.0 \mathrm{mi}, B C=4.0 \mathrm{mi},\) and \(A B=5.0 \mathrm{mi}\) A ship is located at point \(D\) on \(\overline{A B}\) so that \(m \angle A C D=30^{\circ} .\) How far is the ship from the buoy at point \(C ?\) Round your answer to the nearest tenth of a mile.

A surveyor picks two points 250 \(\mathrm{m}\) apart in front of a tall building. The angle of elevation from one point is \(37^{\circ} .\) The angle of elevation from the other point is \(13^{\circ} .\) What is the best estimate for the height of the building? \(\begin{array}{lllll}{\text { A. } 150 \mathrm{m}} & {\text { B. } 138 \mathrm{m}} & {\text { C. } 83 \mathrm{m}} & {\text { D. } 56 \mathrm{m}}\end{array}\)