No 5 the sun, correct to the nearest deflag pole was 44°. If the foot of the pole is25 m from the foot of the building and onthe same horizontal ground, find, correctthat the angle of depression of the top of7 A woman looking out from the window of6 A boy looks through a window of a buildaway from the foot of the building. It wIf the shadow of a pole 7 m high isdepression of the mango from the window.window is 9 m from the ground, caleculatecorrect to the nearest degree, tha angle ofand sees a mango fruit on the ground SO190Essential mathematics for senior secondary schools (2)its length, what is the angle ofy anotherIf the150 m(WAEC)In A WQS using Pythagoras theorem:WS = WQ? + QS²Substituting (i) and (ii) in (iii)e distancethe dA vertical DoA student rthe ais1502=tan 40°tan 35°observes th150 =tan 40°(WASSCE)a building at a height of 30 mtop of theangle of35° Whmoves 10tan 35°122 500=h?observed1(0.839120.70022122 500=h²(0.704122 500 = h²(1.420 + 2.040)0.490313.6 Besto the nearest whole number, the(a) angle of depression of the foot ofpaints andin the aibearings22 500 = 3.46h2A bearing ih2=22 500pole from the woman(b) height of the flag pole. (WASSCE)8 From the top of a building, Deborah observes that the angles of depression of tyevehicles to be 35° and 47°. The two vehicles are on the same straight line with thebuilding and also on the same side of thebuilding. Calculate to the nearest metre theheight of the building if the distancebetween the vehicles is 10 m.9 From a horizontal distance of 8.5 km, a pilot6503 cm3.46h= 6503 m =80.64 mh = 80.6 m to 3 s.f.In compfrom NExercise 13.6pearerFor exIA woman 1.65 m tall stood 50 m away fromthe foot of a tower and observed that theangle of elevation of the top of the towerto be 50°. What is the height of the tower?A young man 1.7 m tall, while standing,measures the angle of elevation of the topof a pole as 40°. If he is 15 m from thepole, what is the height of the pole?3 The angle of depression of a boat from themidpoint of a vertical cliff is 35°. If theboat is 120 m from the foot of the cliff,calculate the height of the cliff. (WASSCE)4The angle of elevation of a tower, 45 m highobserves that the angles of depression ofthe top and base of a control tower are 30°and 33°, respectively. Calculate correct tothree significant figures, the:(a) shortest distance between the pilot andthe base of the control tower(b) height of the control tower. (WAEC)10 (a) The triangle ABC has sidesAB = 17 m, BC = 12 m and AC = 10 m.from a ball on the ground is 52°.(a) How far is the ball from the foot of theCalculate:tower?(b) How much further away should the ball(i) the largest angle of the triangle(ii) the area of the triangle.(b) From a point T on a horizontal ground.be moved from the foot of the tower,so that the angle of elevation is halved?the angle of elevation of the top R oftower RS, 38 m high is 63°. Calcorrect to the nearest metrdistance between T an (WAFrom a po

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5) To find the angle of elevation of sun

5 If the shadow of a pole 7 m high is hat its length, what is the angle of elevai the sun, correct to the nearest From evat Fro