The distance covered by the hiker if he traveled a horizontal distance of 120 ft at and angle of 6° will be given by:
cos θ=adjacent/hypotenuse
let the hypotenuse be h, adjacent =120 ft, θ=6°, thus plugging in the values we shall have:
cos 6=120/h
h=120/cos 6
h=120.661 ft
Answer: 120.661 ft
Answer:
Step-by-step explanation:
1 foot = 12 inches
12 inches/ 48 inches = 1/4 foot
or 1 foot/4 feet = 1/4 foot
Answer:
![b=3\sqrt{13}](https://tex.z-dn.net/?f=b%3D3%5Csqrt%7B13%7D)
Step-by-step explanation:
In a right angled triangle, if a perpendicular is drawn from a vertex of the right angle then triangles on both sides of the perpendicular are similar.
In ΔPDY, ∠D = 90° and DM ⊥ PY
So, ΔPMD ≈ ΔDMY
If two triangles are similar then their corresponding sides are proportional.
![\frac{PM}{DM}=\frac{MD}{MY}](https://tex.z-dn.net/?f=%5Cfrac%7BPM%7D%7BDM%7D%3D%5Cfrac%7BMD%7D%7BMY%7D)
Put ![PM=4\,,\,DM=c\,,\,MD=c\,,\,MY=9](https://tex.z-dn.net/?f=PM%3D4%5C%2C%2C%5C%2CDM%3Dc%5C%2C%2C%5C%2CMD%3Dc%5C%2C%2C%5C%2CMY%3D9)
So,
![\frac{4}{c}=\frac{c}{9}\\\\c=36\\c=6](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7Bc%7D%3D%5Cfrac%7Bc%7D%7B9%7D%5C%5C%5C%5Cc%3D36%5C%5Cc%3D6)
According to Pythagoras theorem, square of hypotenuse is equal to sum of squares of the other two sides.
In ΔDMY,
![DY^2=DM^2+MY^2\\b^2=c^2+9^2](https://tex.z-dn.net/?f=DY%5E2%3DDM%5E2%2BMY%5E2%5C%5Cb%5E2%3Dc%5E2%2B9%5E2)
Put ![c=6](https://tex.z-dn.net/?f=c%3D6)
![b^2=6^2+9^2\\b^2=36+81\\b^2=117\\b=\sqrt{3^2(13)}\\b=3\sqrt{13}](https://tex.z-dn.net/?f=b%5E2%3D6%5E2%2B9%5E2%5C%5Cb%5E2%3D36%2B81%5C%5Cb%5E2%3D117%5C%5Cb%3D%5Csqrt%7B3%5E2%2813%29%7D%5C%5Cb%3D3%5Csqrt%7B13%7D)
26,39,52,65,78,91,104,117,130,143,156,169,182,195,208,221,234,247,260,273,286,299,312,325,338,351,364,377,390,403,416,429,442,455,468,481,494,507,520,<span>533,546,559,572,585,598,611,624,637</span>