Precalculus by Richard Wright

Heaven and earth will pass away, but my words will never pass away. Matthew 24:35 NIV

Take this test as you would take a test in class. When you are finished, check your work against the answers. On this assignment round your answers to three decimal places unless otherwise directed.

- How many triangles are formed with the given information:
*A*= 50˚,*a*= 70,*b*= 100? *A*= 76˚,*B*= 17˚,*c*= 14*A*= 50˚,*a*= 50,*b*= 60*a*= 6,*b*= 9,*c*= 10*A*= 31˚,*b*= 21,*c*= 32- This triangle has two solutions. Find angle
*B*in the second solution:*A*= 80˚,*a*= 69,*b*= 70. - Find the area of the triangle with
*a*= 7,*b*= 13,*c*= 11. Round to two decimal places. - Find the component form of a vector with initial point at (10, 13) and terminal point at (0, 17).
- Find a unit vector in the direction of \(\langle 13, 84 \rangle\).
- \(\overset{\rightharpoonup}{u} + \overset{\rightharpoonup}{v}\)
- \(2\overset{\rightharpoonup}{v}\)
- \(6\overset{\rightharpoonup}{u} - 3\overset{\rightharpoonup}{v}\)
- \(\overset{\rightharpoonup}{u} \cdot \overset{\rightharpoonup}{v}\)
- Find the angle between \(\overset{\rightharpoonup}{u}\) and \(\overset{\rightharpoonup}{v}\).
- Are the vectors \(\langle -2, 4 \rangle\) and \(\langle \frac{1}{2}, -1 \rangle\) orthogonal, parallel, or neither?
- A lawn mower is pushed by exerting a force of 42 pounds on a handle that makes a 30˚ angle with the horizontal ground. Find the work done by pushing the lawn mower 100 feet.
- Write \(z = -9 + 9\sqrt{3}i\) in trigonometric form.
- Write \(z = 25\left(\cos \frac{11π}{6} + i \sin \frac{11π}{6}\right)\) in standard form.
*m*÷*n**m*·*n**n*^{2}- Find the 2nd roots of \(81\left(-\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}i\right)\). Express your answers in standard form rounded to two decimal places.

Solve the triangle with the given information. Round to two decimal places if necessary.

Let \(\overset{\rightharpoonup}{u} = \langle 20, 15 \rangle\) and \(\overset{\rightharpoonup}{v} = \langle -10, 11 \rangle\), find the following.

Given *m* = 10(cos 115˚ + *i* sin 115˚) and *n* = 2(cos 25˚ + *i* sin 25˚), find the following and express your solutions in standard form rounded to two decimal places.

- No triangle
*a*= 13.60,*b*= 4.10,*C*= 87˚*B*_{1}= 66.82˚,*C*_{1}= 63.18˚,*c*_{1}= 58.25;*B*_{2}= 113.18˚,*C*_{2}= 16.82˚,*c*_{2}= 18.88*A*= 36.34˚,*B*= 62.72˚,*C*= 80.94˚*B*= 37.69˚,*C*= 111.31˚,*a*= 17.69- 92.46˚
- 38.50
- \(\langle -10, 4 \rangle\)
- \(\langle \frac{13}{85}, \frac{84}{85} \rangle\)
- \(\langle 10, 26 \rangle\)
- \(\langle -20, 22 \rangle\)
- \(\langle 150, 57 \rangle\)
- −35
- 95.40˚
- Parallel
- 3637.31 ft·lbs
- \(18\left(\cos \frac{2π}{3} + i \sin \frac{2π}{3}\right)\)
- \(\frac{25\sqrt{3}}{2} - \frac{25}{2}i\)
- 5
*i* - −15.32 + 12.86
*i* - 2.57 + 3.06
*i* - 3.44 + 8.31
*i*; −3.44 − 8.31*i*