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Resolución de triángulos 04. En un triángulo ABC, AB = c, AC = by BC = a, se cumple:
a + b4 + c4 = a2(b2 + c2) + c2(a2 + 2b2)
4
01. En un triángulo ABC, AB = c, AC = b Calcule la medida del ángulo C.
y BC = a, se tiene A = 55°, B
= 50° y C = ( 3 + 1) u . Calcule la A) 15° B) 18° C) 22,5°
longitud del radio (en u) de la D) 30° E) 36°
circunferencia circunscrita.
05. Dos embarcaciones parten
A) 2 B) ( 2 + 1) C) 2 2
simultáneamente de un puerto en
direcciones que forman un ángulo
D) ( 3 + 1) E) 3 de 60°, uno a 30 km/h y el otro a 50
km/h. ¿Qué distancia (en km) los
02. Del gráfico, calcule aproxima- separa al cabo de una hora?
damente la medida del ángulo “”.
A) 10 7 B) 10 11 C) 10 13
B D) 10 17 E) 10 19
06. En un triángulo ABC, AB = c, AC = b
y BC = a, reducir la siguiente
expresión:
(a – b2 – c2)tan(A) + (a2 – b2 + c2)tan B
2
2
A C A) – 2 B) – 1 C) 0
D) 1 E) 2
A) 4° B) 8° C) 10° 07. En un triángulo ABC, AB = c, AC = b
D) 15° E) 16° y BC = 5, se cumple que:
C A −B
cot = 5 tan
2 2
03. De acuerdo al gráfico, calcule la Calcule: b
medida del ángulo “”.
A) 4 B) 5 C) 6
B D) 7 E) 8
08. En un triángulo ABC, AB = c, AC = b
x2 + 2x
2x + 3 y BC = a, se cumple que: a = 3b y
A −B A +B
tan + k tan = 1 + 2k
2 2
A C Calcule aproximadamente la
x2 + 3x + 3 medida del ángulo C.
A) 100° B) 105° C) 120° A) 30° B) 37° C) 40°
D) 135° E) 150° D) 45° E) 53°
1
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