Geometry/Trig Name:___________________

Date:___________________ Lesson 10-1: Intro to 3D Trigonometry

Learning Goal #1: What prior knowledge do I need to apply to 3D Trigonometry?

Warm- Up: Recall the following formulas:

Pythagorean Theorem:

We use this when…

Example:

Find the missing side. Show all of your work! Keep

your answer as a radical.

SOH CAH TOA

We use this when…

Example #1: In the right triangle shown in the diagram below, what

is the value of x to the nearest whole number?

Example #2: Solve for the measure of Angle A rounded to the nearest tenth of a degree:

Geometry/Trig Law of Sines:

We use this when…

Example #1: Solve for side AB. to the nearest tenth.

Example #2:

Solve for ∠R to the nearest degree.

Law of Cosines (side):

Law of Cosines (angle):

We use this when…

Example #1:

Given the following measures in DEF, find the length of the third side to the nearest tenth e = 3, f = 5, mD = 58

Example #2: Find the size of the smallest angle to the nearest

degree.

Geometry/Trig Mixed Practice

1. In the diagram below ABEF,. AD = 12 cm, DC = 20 cm and DF = 5 cm. a. Redraw Triangle AFD and label its parts.

b. Calculate the length of AF

c. Calculate the angle between AF and AD to the nearest 10th.

d. Calculate the volume of this triangular prism.

2. The diagram below represents measurements of a triangle plot of land measured by a surveyor. ∠A is 110 ⃘, AB = 600, and ∠B = 25 ⃘.

a. What is the measure of ∠ACB?

b. What is the distance between B and C? Give your answer to the nearest meter.

Geometry/Trig 3. Find the length of the diagonal of the given rectangle. Leave answer in simplest radical form when appropriate.

4. The diagram below shows a plot of land with a fence BD crossing it. AB = 12m, AD = 10m, and ∠BAD = 100 ⃘,

BC = 15m and ∠BDC = 40 ⃘.

a. Find the length of BD to the nearest 10th.

b. Calculate ∠𝐴𝐵𝐷 𝑡𝑜 𝑡ℎ𝑒 𝑛𝑒𝑎𝑟𝑒𝑠𝑡 100𝑡ℎ.

c. If ∠𝐵𝐷𝐶 = 40° and ∠𝐶 = 63°, find the perimeter of ABCD.

Geometry/Trig 5. The following diagram shows a sloping roof. The surface ABCD is a rectangle.

a. Calculate AD to the nearest 100th. You may want to redraw Triangle AFD.

b. What is the length of AB? Write this in your diagram

c. Calculate the length of the diagonal DB to the nearest whole number. You may want to redraw and label Triangle ADB.

d. The length of ED is 4.2. Find the volume of the prism above.

Geometry/Trig 6. The height of a vertical cliff is 450 m. The angle of elevation from a ship to the top of the cliff is 23°. The

ship is x meters from the bottom of the cliff.

(a) Draw a diagram to show this information.

Diagram:

(b) Calculate the value of x to the nearest 10th.

7. The diagram shows a water tower standing on horizontal ground. The height of the tower is 26.5 m. The distance of x is 56.4m.

Find the angle of elevation to the nearest degree.

Ax m