Download In ΔRST, the measure of ∠T=90°, the measure of ∠R=31°, and TR

Name______________________________ Test work due 4/4 at the beginning of the period. Must be
completed by 4/3 at 10PM.
Directions for Take-home test on Delta:
1. Using trig to find a side:
a. Draw a picture and identify the given angle and the sides of the triangles you are using for the trig
function (Label A, H, and O). Label each problem 1-8 and if you get one wrong, you can cross it out
and give the next one the same number.
b. Show the steps you take to get the answer. For example, if you multiply to get your answer, show
what you are multiplying. If you divide to get your answer, show what you are dividing.
Example:
In ΔRST, the measure of ∠T=90°, the measure of ∠R=31°, and TR = 99 feet. Find the length of
RS to the nearest foot.
R
31
𝑥 H
A 99
S CAH
T
2. Using trig to find angles:
a. Draw a picture and identify the given sides of the triangle and the angle you are solving for. Create
the trig function (Label A, H, and O) and then create the inverse trig function. Label each problem
1-7 and if you get one wrong, you can cross it out and give the next one the same number.
b. Show the steps you take to get the answer as shown below.
In ΔTUV, the measure of ∠V=90°, VT = 31 feet, and UV = 92 feet. Find the measure of ∠T to the
nearest tenth of a degree.
T
92
𝑥 = 𝑎𝑟𝑐𝑡𝑎𝑛 ( 31) = 71.37 = 71.4 𝑡𝑜 𝑡ℎ𝑒 𝑛𝑒𝑎𝑟𝑒𝑠𝑡 𝑡𝑒𝑛𝑡ℎ 𝑜𝑓 𝑎 𝑑𝑒𝑔𝑟𝑒𝑒
U
Note arctan and 𝑡𝑎𝑛− 1 are 2 names for the same inverse functions in trig.
TOA 𝑡𝑎𝑛(𝑥 ) = 31
x
92
A 31
V
92
Opp
1
3. Circle Equations with Distance Formula – really Pythagorean’s theorem
a. Draw a picture of the triangle and show your setup with Pythagorean’s formula. Label each
problem 1-7 and if you get one wrong, you can cross it out and give the next one the same number.
Then create the equation for the circle.
Circle equations with distance formula - you have the center and use Pythagorean’s formula to get the
radius
squared:
2
3
Center is (-4, -2). Find the radius using Pythagorean’s
formula. 𝑎2 + 𝑏2 = 𝑐2 or
32 + 22 = 𝑐2 = 13
13 is the 𝑟𝑎𝑑𝑖𝑢𝑠2
The form of the circle equation is
( 𝑥 − 𝑥𝑐𝑒𝑛𝑡𝑒𝑟 )2 + (𝑦 − 𝑦𝑐𝑒𝑛𝑡𝑒𝑟)2 = 𝑟𝑎𝑑𝑖𝑢𝑠2
( 𝑥 + 4 )2 + (𝑦 + 2)2 = 13
The center is (-4, -2) and the radius is √13
You can validate your final equation using Desmos.
4. Finding Circle Center and Radius
a. Move all variable expressions to the left and constants (numbers without variables) to the right.
b. Create the equation of the circle by following the steps below.
c. Label each problem 1-8 and if you get one wrong, you can cross it out and give the next one the
same number.
Example
Complete the square for both x and y. Group the x-terms, y-terms and move the constant to the other side.
2
Follow the steps:
1. Group the terms as follows and move the constant to the other side:
(𝑥2 + 4𝑥) + (𝑦2 − 4𝑦) = 28
Do the first.
2. Take half the constant for the middle term and create the expression using this.
a.
b.
Do the
½ of 4 is 2. Create
on the left.
(you are really adding 4 to both sides)
next.
3. Take half the constant for the middle term and create the expression using this.
a.
b.
. Create
on the left.
.
Simplify the equation
(
Note that the center of this circle is
with a radius of 6.
3