3) Below are two graphed triangles.
a) How long is \(BC\)? How long is \(EF\)?
b) How long is \(AB\)? How long is \(DE\)? (note the circles)
c) What is \(\Large\frac{BC}{AB}\)? What is \(\Large\frac{EF}{DE}\)? What do you notice? Why do they have this relationship?
a) How long is \(BC\)? How long is \(EF\)?
b) How long is \(AB\)? How long is \(DE\)? (note the circles)
c) What is \(\Large\frac{BC}{AB}\)? What is \(\Large\frac{EF}{DE}\)? What do you notice? Why do they have this relationship?
4) Let’s try this again but with different sides.
a) How long is \(AC\)? How long is \(DF\)?
b) How long is \(AB\)? How long is \(DE\)? (note the circles)
c) What is \(\large\frac{AC}{AB}\)? What is \(\large\frac{DF}{DE}\)? What do you notice? Why do they have this relationship?
a) How long is \(AC\)? How long is \(DF\)?
b) How long is \(AB\)? How long is \(DE\)? (note the circles)
c) What is \(\large\frac{AC}{AB}\)? What is \(\large\frac{DF}{DE}\)? What do you notice? Why do they have this relationship?
5) Let’s try one more time with different sides with the above picture
a) How long is \(BC\)? How long is \(EF\)?
b) How long is \(AC\)? How long is \(AF\)? (note the circles)
c) What is \(\Large\frac{BC}{AC}\)? What is \(\Large\frac{EF}{AF}\)? What do you notice? Why do they have this relationship?
a) How long is \(BC\)? How long is \(EF\)?
b) How long is \(AC\)? How long is \(AF\)? (note the circles)
c) What is \(\Large\frac{BC}{AC}\)? What is \(\Large\frac{EF}{AF}\)? What do you notice? Why do they have this relationship?
7) In the picture below, use trigonometry to find the following side lengths. Make sure you first identify the opposite, adjacent, and hypotenuse sides of the indicated angle. Use “SOH CAH TOA” to determine the appropriate trigonometric ratio. Round all answers to the nearest tenth (one decimal point)
a) \(AB=\)
b) \(AC=\)
c) \(DF=\)
d) \(DE=\)
e) \(JH=\)
f) \(GH=\)
g) There are two pairs of answers from problems a-f that are the same. Explain why they are the same.
a) \(AB=\)
b) \(AC=\)
c) \(DF=\)
d) \(DE=\)
e) \(JH=\)
f) \(GH=\)
g) There are two pairs of answers from problems a-f that are the same. Explain why they are the same.
8) In the picture below, \(\triangle ABC\) is dilated by a scale factor of \(2\) from point \(D\) resulting in \(\triangle A’B’C’\). The \(m\angle C = 26.6^{\circ}\).
a) What is \(m\angle B\)?
b) What is \(m\angle B’\)? How do you know?
c) What is the \(m\angle C’\)?
d) Use the distance formula to find the measure of the following sides: \(AB\), \(AC\), \(A'B'\), \(A'C'\).
e) Compare \(\Large\frac{AB}{AC}\) and \(\Large\frac{A'B'}{A'C'}\)
f) Use your calculator (in degree mode) to find sin\((26.6^{\circ})\). What do you notice? Why?
g) Can you confirm “cos\((26.6^{\circ}\))” and “tan(\(26.6^{\circ}\))” using the same method as parts a-e in this problem?
a) What is \(m\angle B\)?
b) What is \(m\angle B’\)? How do you know?
c) What is the \(m\angle C’\)?
d) Use the distance formula to find the measure of the following sides: \(AB\), \(AC\), \(A'B'\), \(A'C'\).
e) Compare \(\Large\frac{AB}{AC}\) and \(\Large\frac{A'B'}{A'C'}\)
f) Use your calculator (in degree mode) to find sin\((26.6^{\circ})\). What do you notice? Why?
g) Can you confirm “cos\((26.6^{\circ}\))” and “tan(\(26.6^{\circ}\))” using the same method as parts a-e in this problem?
9) Local law requires that the base of a telephone pole be at least \(55\) feet above the ground. A local surveyor can figure the height of a pole by measuring the angle a guy wire makes with the ground and the distance the guy wire is attached to the ground away from the base of the pole. Does this pole meet the legal standard?
10) The manufacturer has placed the following labels on a ladder. Under these specifications, what is the highest that this ladder can reach?
11) At a department store, this escalator is \(35\) feet long. Research what typical angle measure of an escalator is.
a) How far horizontally does the escalator span?
b) How high does the escalator ascend?
a) How far horizontally does the escalator span?
b) How high does the escalator ascend?
12) ADA Ramp Specifications require a \(1:12\) wheelchair ramp slope ratio. That is, for every \(1\) unit of rise there must be \(12\) units of run. This amounts to a \(4.8^{\circ}\) incline slope. A construction worker would like to build a ramp to raise a wheelchair user \(2.6\) feet. How long would the ramp be?
Desmos or GeoGebra Challenge
Construct a right triangle and measure the angles and lengths to illustrate the trigonometric ratios.
Solution Bank
Desmos or GeoGebra Challenge
Construct a right triangle and measure the angles and lengths to illustrate the trigonometric ratios.
Solution Bank