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You cannot climb the tower. One angle and one walk still give its height. A walk is a distance along level ground.

Chapter 9 is Some Applications of Trigonometry. It uses the ratios you already know. Recall tan 30° = 1/√3, tan 45° = 1 and tan 60° = √3. Recall sin and cos at these angles too.

Quick catch-up

• The hypotenuse is the side across from the right angle.
• In a right triangle, a² + b² = c². Here c is the hypotenuse.
• Sin, cos and tan divide two sides of a right triangle.
• A right angle is exactly 90°.
• A horizontal line is level, like still water.
• A reading is an angle you measure from one spot.
• A vantage is the spot you look from.
• A pedestal is the stand under a statue.

What this track covers

• The angle you lift — elevation, measured up from the horizontal.
• The angle you lower — depression, and the equal angle at the object.
• Which ratio — the sides you know and want pick it.
• Two posts, one tower — two readings that must give one height.
• One vantage, two lines — a statue on a pedestal.
• Up and down — one window, two triangles.
• Finding the angle — from a height and a shadow.
• The whole solve — read, draw, name, pick, divide, check.

Open the chapter. Read every problem as a right triangle to name.