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3 years ago

Juan construyó una rampa que tiene 5 m de largo y 1 m de altura. ?Cuánto mide la distancia (d) que recorre al subir la rampa

Mathematics

1 answer:

satela [25.4K]3 years ago

7 0

Answer:

$d=\sqrt{26}\ m$ or $d=5.1\ m$

Step-by-step explanation:

<em>The question in English is</em>

Juan built a ramp that is 5 m long and 1 m high. How much is the distance (d) he travels when he climbs the ramp?

let

x -----> the length of the ramp

y ----> the height of the ramp

d ----> the distance Juan travels when he climbs the ramp

we know that

Applying the Pythagoras Theorem

$d^{2}=x^{2}+y^{2}$

we have

$x=5\ m$

$y=1\ m$

substitute the given values

$d^{2}=5^{2}+1^{2}$

$d^{2}=26$

$d=\sqrt{26}\ m$ -----> exact value

$d=5.1\ m$ ----> approximate value

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2 years ago

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Choice A. 3.

Step-by-step explanation:

The triangle in question is a right triangle.

The length of the hypotenuse (the side opposite to the right angle) is given.
The measure of one of the acute angle is also given.

As a result, the length of both legs can be found directly using the sine function and the cosine function.

Let $\text{Opposite}$ denotes the length of the side opposite to the $30^{\circ}$ acute angle, and $\text{Adjacent}$ be the length of the side next to this $30^{\circ}$ acute angle.

$\displaystyle \begin{aligned}\text{Opposite} &= \text{Hypotenuse} \times \sin{30^{\circ}}\\ &=2\sqrt{3}\times \frac{1}{2} \\&= \sqrt{3}\end{aligned}$ .

Similarly,

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The longer leg in this case is the one adjacent to the $30^{\circ}$ acute angle. The answer will be $3$ .

There's a shortcut to the answer. Notice that $\sin{30^{\circ}} < \cos{30^{\circ}}$ . The cosine of an acute angle is directly related to the adjacent leg. In other words, the leg adjacent to the $30^{\circ}$ angle will be the longer leg. There will be no need to find the length of the opposite leg.