# Mathematics Ms Sue help

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You want to estimate the height of the Empire State Building. You start at its base and walk 15 m away. Then you approximate the angle from the ground at that point to the top to be 88 degrees. How tall do you estimate the Empire State Building to be?

• Ms Sue help -

An anchor holding a boat stationary on a river forms a 65 degree angle with the river bottom. The anchor line is 40 meters long. Assuming the river has a uniform depth, how deep is the river directly below the boat?

• Mathematics Ms Sue help -

• Mathematics Ms Sue help -

If you look at your diagram, you should see a right-angled triangle, with base angle 88°, opposite = ? = height

so height/15 = tan88
height = 15tan88 = appr 429.5m

• Mathematics Ms Sue help -

for the building,
h/18 = tan 88°

for the boat,

d/40 = sin 65°

for stuff like this, it always helps to draw a diagram, then dig into your box of trig ratios

• Mathematics Ms Sue help -

For you second question...

this time you know the hypotenuse and the opposite side, so you know you must dealing with the sine ration
sin 65 = height/40
height = 40sin65 = appr 36.25 m

• Mathematics Ms Sue help -

thanks for all you guys helps. drawing shows a better concept then straight digging it thanks

• Mathematics Ms Sue help -

400 m

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