Topic: Right Triangle Problems



Day 2 – Precalculus Topic 15-1: Trigonometry of Right TrianglesElena Gonzálezelena@mcisd.You should already know the definitions (yr, xr, etc)of the trig functions for an angle in standard position, but what if the angle isn't on a graph? What if it's just in a random triangle? Well, there are formulas for that, too.66675124460The Trig Ratio Formulas for Trianglessin=oppositehypotenusecsc=hypotenuseoppositecos=adjacenthypotenusesec=hypotenuseadjacenttan=oppositeadjacentcot=adjacentopposite00The Trig Ratio Formulas for Trianglessin=oppositehypotenusecsc=hypotenuseoppositecos=adjacenthypotenusesec=hypotenuseadjacenttan=oppositeadjacentcot=adjacentoppositeHypotenuse: The longest side, across from the right angleAdjacent: The side next to the angle of interest (usually θ) that isn't the hypotenuseOpposite: The side across from the angle of interest (usually θ)Memory aid for the new definitions:SOH-CAH-TOASOH:sin = oppositehypotenuseCAH:cos = adjacenthypotenuseTOA:tan = oppositeadjacentThe other three functions are still just the reciprocals of these. Once you learn these, the others are easy.Use the appropriate trig function formula to find the length of side b in the triangle below. Show your work!We know the length of the hypotenuse and the size of ∠B. Side b is opposite from ∠B. Therefore, we use the formula for sine.sin ∠B = oppositehypotenuse(plug in the appropriate values)7150404115570abC25°000c = 14 cmBA00abC25°000c = 14 cmBAsin 25° = b14(multiply by 14 on both sides to solve for b)calculator:sin25ENTERx14ENTERRound all angles to the nearest whole degreeRound all other numbers to three decimal placesb = 5.917 cmAngle of elevation or depression: Angle (upward for elevation, downward for depression) between a horizontal line (usually the ground, the horizon, or an imaginary line at the level of the viewer's eyes) and the object of interest. For example, the angle between the surface of the ocean and the position of a submarine, as viewed from a ship.A pilot measures his altitude at 5900 ft as he passes directly over Sears Tower in Chicago. At the same time, the angle of elevation from the end of the runway at O'Hare Airport to the plane is 5.0°. How far is the base of Sears Tower from the end of the runway?tan 5.0 = oppositeadjacent=5900x(tan 5.0)(x) = 5900x = 5900/tan 5.0x = 67437 ft795152070x5900 ft5.0°0x5900 ft5.0°Day 3 – Precalculus Topic 15-1: Trigonometry of Right TrianglesUse trig formulas to solve each problem. Round all angles to the nearest degree. Round all other numbers to three decimal places. Show your work! (Pro tip: Diagrams will help a LOT!)Your cat is trapped in a tree 6.5 m above the ground. Your ladder is 6.7 m long. If you place the tip of the ladder on the branch, what angle will the ladder make with the ground?Commercial airliners fly at an altitude of about 10 km. They start descending toward the airport when they are far away, so that they will not have to dive at a steep angle. If the pilot wants the plane’s path to make an angle of 3° with the ground, at what horizontal distance must she start descending?A submarine at the surface of the ocean makes an emergency dive, its part making an angle of 21° with the surface. If it goes for 300 m along a downward path, how deep will it be?The lid on a grand piano is held open by a prop 28 in long. The base of the prop is 55 in from the lid’s hinge. At what angle will the lid on the piano in #12 open when the prop is placed so that it makes a right angle with the lid?368145478768PianoLidProp00PianoLidProp ................
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