While walking along the a river, Nina wonders what the width of the river is. On further inspection, she finds the angle of depression of the the banks on the opposite sides of the river are 45° and 60°, from a point on the bridge. The height of the bridge is 5 m. She could usetrigonometry to find the solution to this.
River=AD=AB+BDIn ⊿ ABC, ∟A=45°, tan 45°=CB/AB 1=5/AB AB=5mIn ⊿ CBD, ∟D=60°, tan 60°=CB/BD √3=5/BD √3/5=BDAB+BD=5+√3/5 Hence, the river is approximately 5.34 metres.
On the way back home, she saw her sister at the park, she was looking at a slide. Unfortunately the slide was too dirty to ride. To make it useable, Nina need to find a cloth about the length of the slide, she knows that the height of the slide is 3 metres high and the angle of elevation is 45°.
AB=3 m, ∟C=45°, In ⊿ABC, sin 45°= AB/AC 1/√2=3/AC AC=3/√2 AC is approximately 2.12 metres. So she gets a cloth of that length.
While playing Mario Bros. she wonders what the angle of depression would be from the block to Mario the character. She knows that the height of the block is 400 pixels and the length between Mario and the block is 800 pixels.
In ⊿ABC, AB=400 px and AC=800 px. To find ∟CAB, cosθ=AB/AC=400/800=1/2cos 60°=1/2, ∟A=60°, Since, ∟PAB=90, hence ∟PAC=30.