A Ladder and a Secant
Part of the Right-Triangle Trigonometry section of Coddy's Trigonometry journey. Lesson 43 of 50.
A reciprocal ratio often states a comparison directly. A rope that is twice as long as its peg is far from the mast has hypotenuse over adjacent equal to 2, which is sec θ = 2, so cos θ = 1/2 and the rope stands at 60° to the ground.
Off the special values the flip works the same way. If a cable is 1.5 times as long as the distance from its anchor to the pole, sec(theta) = 1.5, so cos θ = 1/1.5 = 2/3 and θ = arccos(2/3), about 48.19°. On the board, Use arcsec: every angle in the domain writes θ = arcsec(1.5) and the round chip finishes it.
Challenge
A ladder is 2.5 times as long as the distance from its foot to the wall, so the angle θ it makes with the ground has sec θ = 2.5. Find θ in degrees, to two decimal places. Then press Check.
Try it yourself
Solve for theta
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Right-Triangle Trigonometry
1Sides of a Right Triangle
How Tall Is the Tree?The HypotenuseThe Opposite SideThe Adjacent SideWhen the Angle MovesRecap: Naming the Sides2The Three Ratios
The Sine RatioThe Cosine RatioThe Tangent RatioChoosing the RatioRecap: The Three Ratios5Finding an Angle
Inverse SineInverse CosineInverse TangentThe Angle of a RampBoth Acute AnglesRecap: Finding an Angle8Reciprocal Ratios
Cosecant, Secant, CotangentExact Reciprocal ValuesA Side From a CosecantA Ladder and a SecantRecap: Reciprocal Ratios