1. Draw First: You cannot solve what you cannot see. Every problem requires a sketch of the triangle.
2. Identify the View: Are you looking up (Elevation) or down (Depression)?
3. Honor the Eye Level: If the problem involves a person standing, you must add their height to the final answer.
4. Show Your Ratio: Write the equation (e.g., $\tan(30) = x / 10$) before you use your calculator.
Using the principle of Similar Triangles (Sun Shadows), calculate the missing heights.
The Cedar and the Staff: A shepherd's staff is 2 meters tall and casts a shadow of 1.5 meters. At the same time, a giant Cedar of Lebanon casts a shadow of 24 meters. How tall is the Cedar?
The Temple Wall: You are standing near the Western Wall. You are 1.6 meters tall, and your shadow is 0.8 meters long. The wall's shadow reaches 10 meters. What is the height of the wall?
Using the Clinometer (Tangent Ratio). Remember: SOH CAH TOA.
The Watchtower: You are standing 50 meters away from the base of a watchtower. You look up at the top with an angle of elevation of $35^\circ$. Your eye level is 1.7 meters from the ground. Find the total height of the tower.
The Kite: You are flying a kite. You have let out 100 meters of string (Hypotenuse). The angle of elevation is $60^\circ$. How high is the kite above the ground? (Assume the string is held at ground level for simplicity, or add hand height if you wish for extra credit).
The Tree Rescue: A cat is stuck in a tree. You place a ladder against the tree. The ladder is 6 meters long (Hypotenuse). For safety, the ladder must make a $70^\circ$ angle with the ground. How high up the tree does the ladder reach?
In the "Kite" problem, why did we use Sine instead of Tangent?
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(Hint: Did we know the distance along the ground, or the length of the string itself?)
Using the "Z" Rule (Alternate Interior Angles).
The Lighthouse: A lighthouse keeper is 40 meters above sea level. He spots a ship. The angle of depression is $12^\circ$. How far is the ship from the base of the lighthouse?
The Cliff Diver: A diver stands on a cliff 25 meters high. He sees a target in the water. The angle of depression is $80^\circ$ (he is looking almost straight down). How far out from the base of the cliff is the target?
You are standing on the roof of Building A (30 meters tall). You look at Building B across the street.
1. You look up at the top of Building B with an angle of elevation of $40^\circ$.
2. You look down at the base of Building B with an angle of depression of $20^\circ$.
Task: Find the height of Building B and the width of the street.
Hint: Use the "Down" triangle first to find the street width. Then use that width to find the "Up" triangle's height. Then add them together.
Objective: Teach a younger sibling (or friend) about the connection between Angle and Length.
Activity: Go outside with a flashlight (or use the sun). Have the younger child stand still.
The Lesson: "Just like the light changes your shadow, God's light changes how big our problems look. If we look at problems with God right above us, the shadows of fear get very small."
Did they understand? [ ] Yes [ ] No
Notes on their reaction: __________________________________________________