Let's solve for f.<span><span><span><span><span><span><span><span>fo</span>r</span>x</span><span>(0.4)</span></span>5</span><span>(<span><span>2x</span>+5</span>)</span></span>−4</span>=1</span>Step 1: Add 4 to both sides.<span><span><span><span><span><span><span><span>0.16f</span>o</span>r</span><span>x2</span></span>+<span><span>25</span><span><span><span>fo</span>r</span>x</span></span></span>−4</span>+4</span>=<span>1+4</span></span><span><span><span><span><span><span>0.16f</span>o</span>r</span><span>x2</span></span>+<span><span>25</span><span><span><span>fo</span>r</span>x</span></span></span>=5</span>Step 2: Factor out variable f.<span><span>f<span>(<span><span><span><span><span>0.8o</span>r</span><span>x2</span></span>+<span><span><span>2o</span>r</span>x</span></span>5</span>)</span></span>=5</span>Step 3: Divide both sides by (0.8orx^2+2orx)/5.<span><span><span>f<span>(<span><span><span><span><span>0.8o</span>r</span><span>x2</span></span>+<span><span><span>2o</span>r</span>x</span></span>5</span>)</span></span><span><span><span><span><span>0.8o</span>r</span><span>x2</span></span>+<span><span><span>2o</span>r</span>x</span></span>5</span></span>=<span>5<span><span><span><span><span>0.8o</span>r</span><span>x2</span></span>+<span><span><span>2o</span>r</span>x</span></span>5</span></span></span><span>f=<span>25<span><span><span><span>0.8o</span>r</span><span>x2</span></span>+<span><span><span>2o</span>r</span>x</span></span></span></span>Answer:<span>f=<span>25<span><span><span><span>0.8o</span>r</span><span>x2</span></span>+<span><span><span>2o</span>r</span><span>x</span></span></span></span></span>
A right triangle is formed with the ladder as the hypotenuse. Since the angle made by the ladder with with ground is given, we can use trigonometric functions to solve for the height of the house.
If we let x be the height of the house and using sine function: sin 24 = x/30 x = 30 sin 24 x = 12.20 ft
