This document calculates the trigonometric ratios of sine, cosine, and tangent for the acute angles (A and B) of the right triangle shown below. It is given that h=4.5cm, a=2.06cm, b=4cm. Using the Pythagorean theorem, it is found that a=2.06cm. The sine, cosine, and tangent are then calculated for angle A, finding that A=27.24°. This process is repeated for angle B, finding that B=62.73°.
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2. Calcula las razones trigonométricas seno, coseno y tangente de los ángulos agudos (A y B) del triángulo rectángulo que aparecen abajo.
Donde el valor de a o el
lado del ángulo que falta la
medida se obtiene por
medio del teorema de
Pitágoras.
h= 𝟒. 𝟓𝒄𝒎
a= 2.06 cm
b=4 cm
𝒉𝟐
= 𝒂𝟐
+ 𝒃𝟐
𝒉𝟐
− 𝒃𝟐
= 𝒂𝟐
𝒂𝟐
= 𝒉𝟐
− 𝒃𝟐
𝒂𝟐
= (𝟒. 𝟓𝒄𝒎)𝟐
−(𝟒𝒄𝒎)𝟐
𝒂𝟐
= 𝟐𝟎. 𝟐𝟓𝒄𝒎𝟐
− 𝟏𝟔𝒄𝒎𝟐
𝒂𝟐
= 𝟒. 𝟐𝟓𝒄𝒎𝟐
𝒂𝟐
= 𝟒. 𝟐𝟓𝒄𝒎
𝒂 = 𝟒. 𝟐𝟓𝒄𝒎 = 𝒄𝒎
𝒂 =2.06m
3. 1
2
.
ℎ = 4.5𝑐𝑚
𝑐𝑜 = 2.06 𝑐𝑚
𝑐𝑎 = 4𝑐𝑚
𝑠𝑒𝑛𝑜 =
𝑐𝑜
ℎ
𝐶𝑜𝑠𝑒𝑛𝑜 =
𝑐𝑎
ℎ
𝑡𝑎𝑛𝑔𝑒𝑛𝑡𝑒 =
𝑐𝑜
𝑐𝑎
se cancela seno a la menos 1 por seno y así mismo con arco
coseno y seno, igualmente para tangente y arco tangente.
𝑠𝑒𝑛𝑜−1
𝑠𝑒𝑛𝑜 𝐴 = 𝑠𝑒𝑛𝑜−1
(
2.06𝑐𝑚
4.5𝑐𝑚
)
𝐴 = 𝑠𝑒𝑛𝑜−1
2.06𝑐𝑚
4.5𝑐𝑚
𝑨 = 𝟐𝟕. 𝟐𝟒°
𝐶𝑜𝑠−1
𝐶𝑜𝑠 𝐴 = 𝐶𝑜𝑠−1
4𝑐𝑚
4.5𝑐𝑚
𝐴 = 𝐶𝑜𝑠−1
4𝐶𝑀
4.5𝐶𝑀
𝑨 = 𝟐𝟕. 𝟐𝟒°
𝑡𝑎𝑛𝑔−1
𝑡𝑎𝑛𝑔 𝐴 = 𝑡𝑎𝑛𝑔−1
2.06𝑐𝑚
4𝑐𝑚
𝐴 = 𝑡𝑎𝑛𝑔−1
2.06𝑐𝑚
4𝑐𝑚
𝑨 = 𝟐𝟕. 𝟐𝟒°
h= 𝟒. 𝟓𝒄𝒎
a= 2.06 cm
b=4 cm
Una vez encontrado el valor del los tres lados
de los triángulos rectángulos para el Angulo
𝜶 𝒚 𝜷 se procede a buscar el seno coseno
tangente.
En primer lugar se empezara con el Angulo A
y posteriormente 𝑩.
4. ℎ = 4.5 𝑐𝑚
𝑐𝑜 = 4𝑐𝑚
𝑐𝑎 = 2.06 𝑐𝑚
𝑠𝑒𝑛𝑜 =
𝑐𝑜
ℎ
𝐶𝑜𝑠𝑒𝑛𝑜 =
𝑐𝑎
ℎ
𝑡𝑎𝑛𝑔𝑒𝑛𝑡𝑒 =
𝑐𝑜
𝑐𝑎
𝑠𝑒𝑛𝑜 𝐵 =
𝑐𝑜
ℎ
𝑠𝑒𝑛𝑜−1
𝑠𝑒𝑛𝑜 𝐵 = 𝑠𝑒𝑛𝑜−1
4𝑐𝑚
4.5𝑐𝑚
𝐵 = 𝑠𝑒𝑛𝑜−1
4𝑐𝑚
4.5𝑐𝑚
𝑩 = 𝟔𝟐. 𝟕𝟑°
𝐶𝑜𝑠−1
𝐶𝑜𝑠 𝐵 = 𝐶𝑜𝑠−1
2.06𝑐𝑚
4.5𝑐𝑚
𝐵 = 𝐶𝑜𝑠−1
2.06𝑐𝑚
4.5𝑐𝑚
𝑩 = 𝟔𝟐, 𝟕𝟑°
𝑡𝑎𝑛𝑔−1
𝑡𝑎𝑛𝑔 𝐵 = 𝑡𝑎𝑛𝑔−1
4𝑐𝑚
2,06𝑐𝑚
𝐵 = 𝑡𝑎𝑛𝑔−1
4𝑐𝑚
2,06𝑐𝑚
𝑩 = 𝟔𝟐. 𝟕𝟑°
1
2
h= 𝟒. 𝟓𝒄𝒎
a= 2.06 cm
b=4 cm
ℎ = 4.5 𝑐𝑚
𝑐𝑜 = 4𝑐𝑚
𝑐𝑎 = 2.06 𝑐𝑚
Una vez encontrado el Angulo A se
realiza la parte b donde encuentra el
valor del Angulo B.para realizar y
obtener el resultado de seno, coseno y
tangente para ello se debe tener
encuentra los valores de la
hipotenusa, cateto opuesto y cateto
adyacente
